Partitioning Method Research Articles

The moss growth optimization (MGO): concepts and performance

Abstract Metaheuristic algorithms are increasingly utilized to solve complex optimization problems because they can efficiently explore large solution spaces. The moss growth optimization (MGO), introduced in this paper, is an algorithm inspired by the moss growth in the natural environment. The MGO algorithm initially determines the evolutionary direction of the population through a mechanism called the determination of wind direction, which employs a method of partitioning the population. Meanwhile, drawing inspiration from the asexual reproduction, sexual reproduction, and vegetative reproduction of moss, two novel search strategies, namely spore dispersal search and dual propagation search, are proposed for exploration and exploitation, respectively. Finally, the cryptobiosis mechanism alters the traditional metaheuristic algorithm’s approach of directly modifying individuals’ solutions, preventing the algorithm from getting trapped in local optima. In experiments, a thorough investigation is undertaken on the characteristics, parameters, and time cost of the MGO algorithm to enhance the understanding of MGO. Subsequently, MGO is compared with 10 original and advanced CEC 2017 and CEC 2022 algorithms to verify its performance advantages. Lastly, this paper applies MGO to four real-world engineering problems to validate its effectiveness and superiority in practical scenarios. The results demonstrate that MGO is a promising algorithm for tackling real challenges. The source codes of the MGO are available at https://aliasgharheidari.com/MGO.html and other websites.

A distributed memory parallel randomized Kaczmarz for sparse system of equations

AbstractKaczmarz algorithm is an iterative projection method for solving system of linear equations that arise in science and engineering problems in various application domains. In addition to classical Kaczmarz, there are randomized and parallel variants. The main challenge of the parallel implementation is the dependency of each Kaczmarz iteration on its predecessor. Because of this dependency, frequent communication is required which results in a substantial overhead. In this study, a new distributed parallel method that reduces the communication overhead is proposed. The proposed method partitions the problem so that the Kaczmarz iterations on different blocks are less dependent. A frequency parameter is introduced to see the effect of communication frequency on the performance. The communication overhead is also decreased by allowing communication between processes only if they have shared non‐zero columns. The experiments are performed using problems from various domains to compare the effects of different partitioning methods on the communication overhead and performance. Finally, parallel speedups of the proposed method on larger problems are presented.

Analysis of Taxi Demand and Traffic Influencing Factors in Urban Core Area Based on Data Field Theory and GWR Model: A Case Study of Beijing

Urban transportation constitutes a complex and dynamic system influenced by various factors, including population density, infrastructure, economic activities, and individual travel behavior. Taxis, as a widespread mode of transportation in many cities, play a crucial role in meeting the transportation needs of urban residents. By using data field theory and the Geographically Weighted Regression (GWR) modeling method, this study explored the complex relationship between taxi demand and traffic-related factors in urban core areas and revealed the potential factors affecting taxi starting and landing points. This research reveals that during the morning peak hours (7:00–9:00), at locations such as long-distance bus terminals, bus stations, parking areas, train stations, and bike-sharing points, taxi demand significantly increases, particularly in the central and southeastern regions of the urban core. Conversely, demand is lower in high-density intersection areas. Additionally, proximity to train stations is positively correlated with higher taxi demand, likely related to the needs of long-distance travelers. During the evening peak hours (17:00–19:00), the taxi demand pattern resembles that of the morning peak, with long-distance bus terminals, bus stations, and parking and bike sharing areas remaining key areas of demand. Notably, parking areas frequently serve as pick-up points for passengers during this time, possibly associated with evening activities and entertainment. Moreover, taxi demand remains high around train stations. In summary, this study enhances our understanding of the dynamics of urban taxi demand and its relationship with various transportation-related influencing factors within the core urban areas. The proposed grid partitioning and GWR modeling methods provide valuable insights for urban transportation planners, taxi service providers, and policymakers, facilitating service optimization and improved urban mobility.

A reliability analysis method based on the intersection area division of hypersphere and paraboloid

In terms of the approximate failure probability of the limit state function (LSF), First Order Reliability Method (FORM) directly solves the failure probability through the most probable point (MPP), but it can only achieve high accuracy in the LSF with low linearity and non-linearity. Second Order Reliability Method (SORM) performs second-order expansion on the basis of MPP to improve reliability accuracy. However, the approximation may be wrong, and even has a large error in high-dimensional nonlinear problems. In order to get more precise approximation of SORM, this paper proposes an area partition method based on the Intersection Area Division Method (IADM) of Hypersphere and Paraboloid. IADM constructs a hypersphere and an approximate parabolic function of the LSF at MPP. The intersection area of the hypersphere and the approximate paraboloid is defined as the failure region from the geometric of the approximate paraboloid function, and the area of the failure region is calculated by the spherical integral. Finally, the approximation of the failure probability is determined by integrating the ratio of the area to the area of the hypersphere. Several examples proved that IADM is more stable compared with SORM which avoids the generation of wrong solutions and improves the accuracy.

One-sweep moment-based semi-implicit-explicit integration for gray thermal radiation transport

Thermal radiation transport (TRT) is a time dependent, high dimensional partial integro-differential equation. In practical applications such as inertial confinement fusion, TRT is coupled to other physics such as hydrodynamics, plasmas, etc., and the timescales one is interested in capturing are often much slower than the radiation timescale. As a result, TRT is treated implicitly, and due to its stiffness and high dimensionality, is often a dominant computational cost in multiphysics simulations. Here we develop a new approach for implicit-explicit (IMEX) integration of gray TRT in the deterministic SN setting, which requires only one sweep per stage, with the simplest first-order method requiring only one sweep per time step. The partitioning of equations is done via a moment-based high-order low-order formulation of TRT, where the streaming operator and first two moments are used to capture the asymptotic stiff regimes of the streaming limit and diffusion limit. Absorption-reemission is treated explicitly, and although stiff, is sufficiently damped by the implicit solve that we achieve stable accurate time integration without incorporating the coupling of the high order and low order equations implicitly. Due to nonlinear coupling of the high-order and low-order equations through temperature-dependent opacities, to facilitate IMEX partitioning and higher-order methods, we use a semi-implicit integration approach amenable to nonlinear partitions. Results are demonstrated on thick Marshak and crooked pipe benchmark problems, demonstrating orders of magnitude improvement in accuracy and wallclock compared with the standard first-order implicit integration typically used.

Physics-Informed Neural Networks for Prediction of a Flow-Induced Vibration Cylinder

Abstract Flow-induced vibration (FIV) is a common phenomenon in ocean engineering for subsea structures with circular-shaped cross sections. A large amount of computational resources or experimental efforts are required to predict or measure the complicated motions and flow field surrounding a circular cylinder undergoing vortex-induced vibration (VIV). Physics-informed neural networks (PINNs) are powerful deep learning techniques for solving governing partial differential equations (PDEs) of dynamic systems as an alternative to complex numerical methods. In the present study, a framework is built employing PINNs for solving the Navier–Stokes equations to predict flows past an FIV cylinder using sparsely distributed spatiotemporal data inside the domain. The training process involves minimizing the supervised loss of flow data at these sparse points and the residuals of the governing PDEs. For the training of the PINN model, a moving frame around an FIV cylinder is used to collect the training flow data from two-dimensional direct numerical simulation results at a low Reynolds number. The structural displacements of the cylinder are also implemented in the residuals of the equations of the developed PINN. The performance of the PINN is evaluated by comparing the predicted contours of the surrounding flow velocities with the training data. The hydrodynamic forces prediction is achieved using the PINN-obtained flow field predictions combined with the force partitioning method.

Retinal microvascular changes in patients with pancreatitis and their clinical significance

Acute pancreatitis, a common exocrine inflammatory disease affecting the pancreas, is characterized by intense abdominal pain and multiple organ dysfunction. However, the alterations in retinal blood vessels among individuals with acute pancreatitis remain poorly understood. This study employed optical coherence tomography angiography (OCTA) to examine the superficial and deep retinal blood vessels in patients with pancreatitis. Sixteen patients diagnosed with pancreatitis (32 eyes) and 16 healthy controls (32 eyes) were recruited from the First Affiliated Hospital of Nanchang University for participation in the study. Various ophthalmic parameters, such as visual acuity, intraocular pressure, and OCTA image for retina consisting of the superficial retinal layer (SRL) and the deep retinal layer (DRL), were recorded for each eye. The study observed the superficial and deep retinal microvascular ring (MIR), macrovascular ring (MAR), and total microvessels (TMI) were observed. Changes in retinal vascular density in the macula through annular partitioning (C1–C6), hemispheric quadrant partitioning (SR, SL, IL, and IR), and early diabetic retinopathy treatment studies (ETDRS) partitioning methods (R, S, L, and I). Correlation analysis was employed to investigate the relationship between retinal capillary density and clinical indicators. Our study revealed that in the superficial retinal layer, the vascular density of TMI, MIR, MAR, SR, IR, S, C2, C3 regions were significantly decreased in patients group compared with the normal group. For the deep retinal layer, the vascular density of MIR, SR, S, C1, C2 regions also reduced in patient group. The ROC analysis demonstrated that OCTA possesses significant diagnostic performance for pancreatitis. In conclusion, patients with pancreatitis may have retinal microvascular dysfunction, and OCTA can be a valuable tool for detecting alterations in ocular microcirculation in pancreatitis patients in clinical practice.

A novel density‐based representation for point cloud and its ability to facilitate classification

AbstractCurrently, in the field of processing 3D point cloud data, two primary representation methods have emerged: point‐based methods and voxel‐based methods. However, the former suffer from significant computational costs and lack the ease of handling exhibited by voxel‐based methods. Conversely, the later often encounter challenges related to information loss resulting from downsampling operations, thereby impeding subsequent tasks. To address these limitations, this article introduces a novel density‐based representation method for voxel partitioning. Additionally, a corresponding network structure is devised to extract features from this specific density representation, thereby facilitating the successful completion of classification tasks. The experiments are implemented on ModelNet40 and MNIST demonstrate that the proposed 3D convolution can achieve the‐state‐of‐the‐art performance based on the voxels.

Climate factors dominate the elevational variation in grassland plant resource utilization strategies.

Specific leaf area (SLA) and leaf dry matter content (LDMC) are key leaf functional traits often used to reflect plant resource utilization strategies and predict plant responses to environmental changes. In general, grassland plants at different elevations exhibit varying survival strategies. However, it remains unclear how grassland plants adapt to changes in elevation and their driving factors. To address this issue, we utilized SLA and LDMC data of grassland plants from 223 study sites at different elevations in China, along with climate and soil data, to investigate variations in resource utilization strategies of grassland plants along different elevational gradients and their dominant influencing factors employing linear mixed-effects models, variance partitioning method, piecewise Structural Equation Modeling, etc. The results show that with increasing elevation, SLA significantly decreases, and LDMC significantly increases (P < 0.001). This indicates different resource utilization strategies of grassland plants across elevation gradients, transitioning from a "faster investment-return" at lower elevations to a "slower investment-return" at higher elevations. Across different elevation gradients, climatic factors are the main factors affecting grassland plant resource utilization strategies, with soil nutrient factors also playing a non-negligible coordinating role. Among these, mean annual precipitation and hottest month mean temperature are key climatic factors influencing SLA of grassland plants, explaining 28.94% and 23.88% of SLA variation, respectively. The key factors affecting LDMC of grassland plants are mainly hottest month mean temperature and soil phosphorus content, with relative importance of 24.24% and 20.27%, respectively. Additionally, the direct effect of elevation on grassland plant resource utilization strategies is greater than its indirect effect (through influencing climatic and soil nutrient factors). These findings emphasize the substantive impact of elevation on grassland plant resource utilization strategies and have important ecological value for grassland management and protection under global change.

Process Optimization and Characterization of Polysaccharides with Potential Antioxidant and Hypoglycemic Activity from Cissus repens.

Ultrasound-assisted extraction of Cissus repens polysaccharides (CRPs) was optimized through response surface methodology (RSM) based on Box-Behnken design (BBD). The maximum CRPs yield (16.18 %) was achieved under the optimum extraction conditions: extraction time 72 min, extraction temperature 74 °C, extraction power 240 W. Then three-phase partitioning (TPP) method combined with gradient alcohol precipitation was used to obtained CRP20, CRP40, CRP60 and CRP80 from CRPs, and CRP80 has a higher purity than others. The primary chemical and structural characteristics of CRP80 were investigated by UV, FT-IR, high-performance liquid chromatography (HPLC) and high-performance gel-permeation chromatography (HPGPC). CRP80 is mainly composed of glucose, galactose, arabinose and mannose, with a molecular weights of approximately 2.95 kDa. Furthermore, the antioxidant activity and hypoglyceamic activity of CRP80 in vitro were evaluated. The results showed that CRP80 had strong scavenging activities on ABTS, hydroxyl and DPPH radicals, as well as high scavenging activities on α-glucosidase and α-amylase. Our research provided an efficient method for the extraction of polysaccharides from C. repens and CRP80 has potential as a promising source of natural antioxidants and hypoglycemic agent for the functional food and medicinal industries.

Resiliency planning of distribution network using of active distribution network partitioning

Today, micro-grids (MGs) include all kinds of energy storage systems (ESSs), wind turbines (WTs), photovoltaic (PV), combined heat and power (CHP), etc., also demand response are active on the demand side. In this paper, single-level robust methods for partitioning and planning the active distribution network (ADN) into several MGs are presented. According to the desired purpose, the objective function of the model is investment costs minimization for installing the capacity of distributed generations (DGs) and switches, the activity of responsive loads based on the forecast of the generation of non- DG, losses and the risk of the load points of the costumers. On the other hand, maximizing the income from the MGs energy sales to the upstream grid and the technical constraints include optimal power flow (OPF) equations. The mentioned problem is a complex nonlinear model, and therefore, the improved genetic algorithm (GA) is used. In order to validate the efficiency, the improved method has been used on a 25-bus ADN including five switches. The simulation results obtained from the case studies prove the fact that the use of the retrofitted model increases the investment costs of the MG, especially in the case of an island operation, in contrast to the active presence of responsive loads that significantly reduce costs.

Active distribution network dynamic partitioning method based on the Voltage/Var sensitivity using branch cutting and binary particle swarm optimisation

AbstractTo optimally harness the adjustable capabilities of reactive power sources for voltage control, a dynamic partitioning method that uses reactive power flow tracking for branch cutting through Binary Particle Swarm Optimisation (BPSO) is proposed for Active Distribution Networks (ADNs). Initially, the limitations of existing Voltage/Var Sensitivity (VVS) calculation methods are analysed, leading to the proposition of a novel VVS calculation method capable of capturing variations in source‐load timing characteristics. Subsequently, the fuzzification of the VVS matrix between nodes is used to derive the membership degree matrix. Next, based on the membership relationship between reactive power source nodes, these nodes are pre‐partitioned, and the number of leading nodes and zones alongside are preliminarily determined. Then, the range of the branch to be cut is established, guided by the reactive power flow direction of the branch. Employing the zonal comprehensive coupling degree as the objective function of the BPSO facilitates the identification of optimal branch cutting points, thereby determining the partitioning outcome. Finally, a reactive power reserve check is executed to rectify any non‐compliant zones. In this study, numerical simulations are conducted using the enhanced IEEE 33‐node power system to demonstrate the efficacy of the proposed method.

Evaluation of serum mid-infrared spectroscopy as new prognostic marker for first-line bevacizumab-based chemotherapy in metastatic colorectal cancer

Background and aimsBevacizumab-based chemotherapy is a recommended first-line treatment for metastatic colorectal cancer (mCRC). Robust biomarkers with clinical practice applicability have not been identified for patients with this treatment. We aimed to evaluate the prognostic yield of serum mid-infrared spectroscopy (MIRS) on patients receiving first-line bevacizumab-based chemotherapy for mCRC. MethodsWe conducted an ancillary analysis from a multicentre prospective study (NCT00489697). All baseline serums were screened by attenuated total reflection method. Principal component analysis and unsupervised k-mean partitioning methods were performed blinded to all patients’ data. Endpoints were progression-free survival (PFS) and overall survival (OS). ResultsFrom the 108 included patients, MIRS discriminated two prognostic groups. First group patients had significantly lower body mass index (p = 0.026) and albumin levels (p < 0.001), and higher levels of angiogenic markers, lactate dehydrogenase and carcinoembryonic antigen (p < 0.001). In univariate analysis, their OS and PFS were shorter with respective medians: 17.6 vs 27.9 months (p = 0.02) and 8.7 vs 11.3 months (p = 0.03). In multivariate analysis, PFS was significantly shorter (HR = 1.74, p = 0.025) with a similar trend for OS (HR = 1.69, p = 0.061). ConclusionBy metabolomic fingerprinting, MIRS proves to be a promising prognostic tool for patients receiving first-line bevacizumab-based chemotherapy for mCRC.

Spatial Query Optimization With Learning

Query optimization is a key component in database management systems (DBMS) and distributed data processing platforms. Recent research in the database community incorporated techniques from artificial intelligence to enhance query optimization. Various learning models have been extended and applied to the query optimization tasks, including query execution plan, query rewriting, and cost estimation. The tasks involved in query optimization differ based on the type of data being processed, such as relational data or spatial geometries. This tutorial reviews recent learning-based approaches for spatial query optimization tasks. We go over methods designed specifically for spatial data, as well as solutions proposed for high-dimensional data. Additionally, we present learning-based spatial indexing and spatial partitioning methods, which are also vital components in spatial data processing. We also identify several open research problems in these fields.

A method to shorten the time of high-dimensional matrix operations and convolution operations

Serverless computing, or Function-as-a-Service (FaaS), is a cloud computing execution model where the cloud provider dynamically manages the allocation and provisioning of servers which is a new way to solve the problem that the need of client.By serverless computing clients can easily solve their problems anytime,anywhere.However, the complex convolution operations and high-dimensional matrix operations can still consume a lot of resources such as computation time and memory occupancy in serverless computing. In this paper, firstly, the author selects two frequently used models in serverless computing, and then divide them into different numbers of partitions respectively to study the impact of partitioning methods on the computation time and memory occupancy. The author show that different partitioning methods can make an obviously impact on the computation time and memory occupancy,whitch shows that the proper partitioning of high-dimensional matrices and tensors can make a significantly reduction of calculation time and memory occupancy.

Relation coarsest partition method to observability of probabilistic Boolean networks

Using the relational coarsest partition (RCP) method, this article aims to study the observability problem of probabilistic Boolean networks (PBNs). The key step to solving this problem is to find the parallel cycle and the coarsest refinement partition of the given initial partition. Firstly, several definitions of observability for PBNs are proposed, and the connections between finite-time observability with positive probability (FTOPP), asymptotical observability (AO), and finite-time observability with probability one (FTOPO) are revealed. Secondly, by defining the appropriate transition relation, the RCP method is introduced into PBNs. In addition, based on the output signal mapping set, the initial partition is constructed. Thirdly, the concept of a parallel cycle for PBNs is proposed, and two algorithms are presented for computing the cycle and parallel cycle of PBNs. Moreover, with the help of the RCP method, a series of criteria are derived to solve the observability problem of PBNs, which works more efficiently. Fourth, when PBN is unobservable, an algorithm is proposed to design the state-flipping set with the smallest number of states, which can make the unobservable PBN observable. To show the validity and effectiveness of the obtained results, examples are finally given.

Areal and phylogenetic dimensions of word order variation in Indo-European languages

Abstract Both areal and phylogenetic affiliation have been discussed as driving factors of the distribution of word order in the languages of the world. However, disentangling the interaction of these two factors is challenging. Here we take Indo-European as a test case. Word order in this family is largely homogeneous both within areas and within branches, which makes it difficult to assess which factor was more important in shaping the present-day distribution. To break out of this impasse we turn to corpus data and explicit statistical modeling. Building on a parallel corpus of movie subtitles, we investigate word order on the sentence level under stable pragmatic conditions. We measure the similarity of word order variation between pairs of languages with an information-theoretic distance metric. Using cluster analysis and variation partitioning methods these distance metrics show that phylogenetic distance predicts more variation than geographical distance, but the most important predictor is the shared fraction where phylogeny and area overlap. We conclude that word order has evolved along both dimensions and cannot be reduced to a single one.

Exploration of Free Energy Surface of the Au10 Nanocluster at Finite Temperature.

The first step in comprehending the properties of Au10 clusters is understanding the lowest energy structure at low and high temperatures. Functional materials operate at finite temperatures; however, energy computations employing density functional theory (DFT) methodology are typically carried out at zero temperature, leaving many properties unexplored. This study explored the potential and free energy surface of the neutral Au10 nanocluster at a finite temperature, employing a genetic algorithm coupled with DFT and nanothermodynamics. Furthermore, we computed the thermal population and infrared Boltzmann spectrum at a finite temperature and compared it with the validated experimental data. Moreover, we performed the chemical bonding analysis using the quantum theory of atoms in molecules (QTAIM) approach and the adaptive natural density partitioning method (AdNDP) to shed light on the bonding of Au atoms in the low-energy structures. In the calculations, we take into consideration the relativistic effects through the zero-order regular approximation (ZORA), the dispersion through Grimme's dispersion with Becke-Johnson damping (D3BJ), and we employed nanothermodynamics to consider temperature contributions. Small Au clusters prefer the planar shape, and the transition from 2D to 3D could take place at atomic clusters consisting of ten atoms, which could be affected by temperature, relativistic effects, and dispersion. We analyzed the energetic ordering of structures calculated using DFT with ZORA and single-point energy calculation employing the DLPNO-CCSD(T) methodology. Our findings indicate that the planar lowest energy structure computed with DFT is not the lowest energy structure computed at the DLPN0-CCSD(T) level of theory. The computed thermal population indicates that the 2D elongated hexagon configuration strongly dominates at a temperature range of 50-800 K. Based on the thermal population, at a temperature of 100 K, the computed IR Boltzmann spectrum agrees with the experimental IR spectrum. The chemical bonding analysis on the lowest energy structure indicates that the cluster bond is due only to the electrons of the 6 s orbital, and the Au d orbitals do not participate in the bonding of this system.

Aptamer Screening: Current Methods and Future Trend towards Non-SELEX Approach.

Aptamers are nucleic acid sequences that specifically bind with target molecules and are vital to applications such as biosensing, drug development, disease diagnostics, etc. The traditional selection procedure of aptamers is based on the Systematic Evolution of Ligands by an Exponential Enrichment (SELEX) process, which relies on repeating cycles of screening and amplification. With the rapid development of aptamer applications, RNA and XNA aptamers draw more attention than before. But their selection is troublesome due to the necessary reverse transcription and transcription process (RNA) or low efficiency and accuracy of enzymes for amplification (XNA). In light of this, we review the recent advances in aptamer selection methods and give an outlook on future development in a non-SELEX approach, which simplifies the procedure and reduces the experimental costs. We first provide an overview of the traditional SELEX methods mostly designed for screening DNA aptamers to introduce the common tools and methods. Then a section on the current screening methods for RNA and XNA is prepared to demonstrate the efforts put into screening these aptamers and the current difficulties. We further predict that the future trend of aptamer selection lies in non-SELEX methods that do not require nucleic acid amplification. We divide non-SELEX methods into an immobilized format and non-immobilized format and discuss how high-resolution partitioning methods could facilitate the further improvement of selection efficiency and accuracy.

Evaluation of heritability partitioning approaches in livestock populations

BackgroundHeritability partitioning approaches estimate the contribution of different functional classes, such as coding or regulatory variants, to the genetic variance. This information allows a better understanding of the genetic architecture of complex traits, including complex diseases, but can also help improve the accuracy of genomic selection in livestock species. However, methods have mainly been tested on human genomic data, whereas livestock populations have specific characteristics, such as high levels of relatedness, small effective population size or long-range levels of linkage disequilibrium.ResultsHere, we used data from 14,762 cows, imputed at the whole-genome sequence level for 11,537,240 variants, to simulate traits in a typical livestock population and evaluate the accuracy of two state-of-the-art heritability partitioning methods, GREML and a Bayesian mixture model. In simulations where a single functional class had increased contribution to heritability, we observed that the estimators were unbiased but had low precision. When causal variants were enriched in variants with low (< 0.05) or high (> 0.20) minor allele frequency or low (below 1st quartile) or high (above 3rd quartile) linkage disequilibrium scores, it was necessary to partition the genetic variance into multiple classes defined on the basis of allele frequencies or LD scores to obtain unbiased results. When multiple functional classes had variable contributions to heritability, estimators showed higher levels of variation and confounding between certain categories was observed. In addition, estimators from small categories were particularly imprecise. However, the estimates and their ranking were still informative about the contribution of the classes. We also demonstrated that using methods that estimate the contribution of a single category at a time, a commonly used approach, results in an overestimation. Finally, we applied the methods to phenotypes for muscular development and height and estimated that, on average, variants in open chromatin regions had a higher contribution to the genetic variance (> 45%), while variants in coding regions had the strongest individual effects (> 25-fold enrichment on average). Conversely, variants in intergenic or intronic regions showed lower levels of enrichment (0.2 and 0.6-fold on average, respectively).ConclusionsHeritability partitioning approaches should be used cautiously in livestock populations, in particular for small categories. Two-component approaches that fit only one functional category at a time lead to biased estimators and should not be used.