Optimal investment based on relative performance and weighted utility

This paper studies the optimal portfolio allocation of a fund manager when he bases decisions on both the absolute level of terminal relative performance and the change value of terminal relative performance comparison to a predefined reference point. We find the optimal investment strategy by maximizing a weighted average utility of a concave utility and an Sshaped utility via a concavification technique and the martingale method. Numerical results are carried out to show the impact of the extent to which the manager pays attention to the change of relative performance related to the reference point on the optimal terminal relative performance.

The Weighted Basis for PHT-Splines

PHT-splines are defined as polynomial splines over hierarchical T-meshes with very efficient local refinement properties.The original PHT-spline basis functions constructed by the truncation mechanism have a decay phenomenon,resulting in numerical instability.The non-decay basis functions are constructed as the B-splines that are defined on the 2×2 tensor product meshes associated with basis vertices in Kang et al.,but at the cost of losing the partition of unity.In the field of finite element analysis and topology optimization,forming the partition of unity is the default ingredient for constructing basis functions of approximate spaces.In this paper,we will show that the non-decay PHT-spline basis functions proposed by Kang et al.can be appropriately modified to form a partition of unity.Each non-decay basis function is multiplied by a positive weight to form the weighted basis.The weights are solved such that the sum of weighted bases is equal to 1 on the domain.We provide two methods for calculatingweights,based on geometric information of basis functions and the subdivision of PHT-splines.Weights are given in the form of explicit formulas and can be efficiently calculated.We also prove that the weights on the admissible hierarchical T-meshes are positive.

An Improved Solov2 Based on Attention Mechanism and Weighted Loss Function for Electrical Equipment Instance Segmentation

The current existing problem of deep learning framework for the detection and segmentation of electrical equipment is dominantly related to low precision.Because of the reliable,safe and easy-to-operate technology provided by deep learning-based video surveillance for unmanned inspection of electrical equipment,this paper uses the bottleneck attention module(BAM)attention mechanism to improve the Solov2 model and proposes a new electrical equipment segmentation mode.Firstly,the BAM attention mechanism is integrated into the feature extraction network to adaptively learn the correlation between feature channels,thereby improving the expression ability of the feature map;secondly,the weighted sum of CrossEntropy Loss and Dice loss is designed as the mask loss to improve the segmentation accuracy and robustness of the model;finally,the non-maximal suppression(NMS)algorithm to better handle the overlap problem in instance segmentation.Experimental results show that the proposed method achieves an average segmentation accuracy of mAP of 80.4% on three types of electrical equipment datasets,including transformers,insulators and voltage transformers,which improve the detection accuracy by more than 5.7% compared with the original Solov2 model.The segmentation model proposed can provide a focusing technical means for the intelligent management of power systems.

Geographically and Temporally Weighted Regression in Assessing Dengue Fever Spread Factors in Yunnan Border Regions

Objective This study employs the Geographically and Temporally Weighted Regression(GTWR)model to assess the impact of meteorological elements and imported cases on dengue fever outbreaks,emphasizing the spatial-temporal variability of these factors in border regions.Methods We conducted a descriptive analysis of dengue fever’s temporal-spatial distribution in Yunnan border areas.Utilizing annual data from 2013 to 2019,with each county in the Yunnan border serving as a spatial unit,we constructed a GTWR model to investigate the determinants of dengue fever and their spatio-temporal heterogeneity in this region.Results The GTWR model,proving more effective than Ordinary Least Squares(OLS)analysis,identified significant spatial and temporal heterogeneity in factors influencing dengue fever’s spread along the Yunnan border.Notably,the GTWR model revealed a substantial variation in the relationship between indigenous dengue fever incidence,meteorological variables,and imported cases across different counties.Conclusion In the Yunnan border areas,local dengue incidence is affected by temperature,humidity,precipitation,wind speed,and imported cases,with these factors’influence exhibiting notable spatial and temporal variation.

Unsupervised Color Segmentation with Reconstructed Spatial Weighted Gaussian Mixture Model and Random Color Histogram

Image classification and unsupervised image segmentation can be achieved using the Gaussian mixture model.Although the Gaussian mixture model enhances the flexibility of image segmentation,it does not reflect spatial information and is sensitive to the segmentation parameter.In this study,we first present an efficient algorithm that incorporates spatial information into the Gaussian mixture model(GMM)without parameter estimation.The proposed model highlights the residual region with considerable information and constructs color saliency.Second,we incorporate the content-based color saliency as spatial information in the Gaussian mixture model.The segmentation is performed by clustering each pixel into an appropriate component according to the expectation maximization and maximum criteria.Finally,the random color histogram assigns a unique color to each cluster and creates an attractive color by default for segmentation.A random color histogram serves as an effective tool for data visualization and is instrumental in the creation of generative art,facilitating both analytical and aesthetic objectives.For experiments,we have used the Berkeley segmentation dataset BSDS-500 and Microsoft Research in Cambridge dataset.In the study,the proposed model showcases notable advancements in unsupervised image segmentation,with probabilistic rand index(PRI)values reaching 0.80,BDE scores as low as 12.25 and 12.02,compactness variations at 0.59 and 0.7,and variation of information(VI)reduced to 2.0 and 1.49 for the BSDS-500 and MSRC datasets,respectively,outperforming current leading-edge methods and yielding more precise segmentations.

Algorithms and statistical analysis for linear structured weighted total least squares problem

Weighted total least squares(WTLS)have been regarded as the standard tool for the errors-in-variables(EIV)model in which all the elements in the observation vector and the coefficient matrix are contaminated with random errors.However,in many geodetic applications,some elements are error-free and some random observations appear repeatedly in different positions in the augmented coefficient matrix.It is called the linear structured EIV(LSEIV)model.Two kinds of methods are proposed for the LSEIV model from functional and stochastic modifications.On the one hand,the functional part of the LSEIV model is modified into the errors-in-observations(EIO)model.On the other hand,the stochastic model is modified by applying the Moore-Penrose inverse of the cofactor matrix.The algorithms are derived through the Lagrange multipliers method and linear approximation.The estimation principles and iterative formula of the parameters are proven to be consistent.The first-order approximate variance-covariance matrix(VCM)of the parameters is also derived.A numerical example is given to compare the performances of our proposed three algorithms with the STLS approach.Afterwards,the least squares(LS),total least squares(TLS)and linear structured weighted total least squares(LSWTLS)solutions are compared and the accuracy evaluation formula is proven to be feasible and effective.Finally,the LSWTLS is applied to the field of deformation analysis,which yields a better result than the traditional LS and TLS estimations.

THE BOUNDEDNESS OF OPERATORS ON WEIGHTED MULTI-PARAMETER LOCAL HARDY SPACES

Though atomic decomposition is a very useful tool for studying the boundedness on Hardy spaces for some sublinear operators,untill now,the boundedness of operators on weighted Hardy spaces in a multi-parameter setting has been established only by almost orthogonality estimates.In this paper,we mainly establish the boundedness on weighted multi-parameter local Hardy spaces via atomic decomposition.

Large-Scale Multi-Objective Optimization Algorithm Based on Weighted Overlapping Grouping of Decision Variables

The large-scale multi-objective optimization algorithm(LSMOA),based on the grouping of decision variables,is an advanced method for handling high-dimensional decision variables.However,in practical problems,the interaction among decision variables is intricate,leading to large group sizes and suboptimal optimization effects;hence a large-scale multi-objective optimization algorithm based on weighted overlapping grouping of decision variables(MOEAWOD)is proposed in this paper.Initially,the decision variables are perturbed and categorized into convergence and diversity variables;subsequently,the convergence variables are subdivided into groups based on the interactions among different decision variables.If the size of a group surpasses the set threshold,that group undergoes a process of weighting and overlapping grouping.Specifically,the interaction strength is evaluated based on the interaction frequency and number of objectives among various decision variables.The decision variable with the highest interaction in the group is identified and disregarded,and the remaining variables are then reclassified into subgroups.Finally,the decision variable with the strongest interaction is added to each subgroup.MOEAWOD minimizes the interactivity between different groups and maximizes the interactivity of decision variables within groups,which contributed to the optimized direction of convergence and diversity exploration with different groups.MOEAWOD was subjected to testing on 18 benchmark large-scale optimization problems,and the experimental results demonstrate the effectiveness of our methods.Compared with the other algorithms,our method is still at an advantage.

Operational optimization of copper flotation process based on the weighted Gaussian process regression and index-oriented adaptive differential evolution algorithm

Concentrate copper grade(CCG)is one of the important production indicators of copper flotation processes,and keeping the CCG at the set value is of great significance to the economic benefit of copper flotation industrial processes.This paper addresses the fluctuation problem of CCG through an operational optimization method.Firstly,a density-based affinity propagationalgorithm is proposed so that more ideal working condition categories can be obtained for the complex raw ore properties.Next,a Bayesian network(BN)is applied to explore the relationship between the operational variables and the CCG.Based on the analysis results of BN,a weighted Gaussian process regression model is constructed to predict the CCG that a higher prediction accuracy can be obtained.To ensure the predicted CCG is close to the set value with a smaller magnitude of the operation adjustments and a smaller uncertainty of the prediction results,an index-oriented adaptive differential evolution(IOADE)algorithm is proposed,and the convergence performance of IOADE is superior to the traditional differential evolution and adaptive differential evolution methods.Finally,the effectiveness and feasibility of the proposed methods are verified by the experiments on a copper flotation industrial process.

THE WEIGHTED KATO SQUARE ROOT PROBLEMOF ELLIPTIC OPERATORS HAVING A BMOANTI-SYMMETRICPART

Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted Kato square root problem for L.More precisely,we prove that the square root L^(1/2)satisfies the weighted L^(p)estimates||L^(1/2)(f)||L_(ω)^p(R^(n))≤C||■f||L_(ω)^p(R^(n);R^(n))for any p∈(1,∞)andω∈Ap(ℝ^(n))(the class of Muckenhoupt weights),and that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,2+ε)andω∈Ap(ℝ^(n))∩RH_(2+ε/p),(R^(n))(the class of reverse Hölder weights),whereε∈(0,∞)is a constant depending only on n and the operator L,and where(2+ε/p)'denotes the Hölder conjugate exponent of 2+ε/p.Moreover,for any given q∈(2,∞),we give a sufficient condition to obtain that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,q)andω∈A_(p)(R^(n))∩pRH_(q/p),(R^(n)).As an application,we prove that when the coefficient matrix A that appears in L satisfies the small BMO condition,the Riesz transform∇L^(−1/2)is bounded on L_(ω)^(p)(ℝ^(n))for any given p∈(1,∞)andω∈Ap(ℝ^(n)).Furthermore,applications to the weighted L^(2)-regularity problem with the Dirichlet or the Neumann boundary condition are also given.

Screening biomarkers for spinal cord injury using weighted gene co-expression network analysis and machine learning

Immune changes and inflammatory responses have been identified as central events in the pathological process of spinal co rd injury.They can greatly affect nerve regeneration and functional recovery.However,there is still limited understanding of the peripheral immune inflammato ry response in spinal cord inju ry.In this study.we obtained microRNA expression profiles from the peripheral blood of patients with spinal co rd injury using high-throughput sequencing.We also obtained the mRNA expression profile of spinal cord injury patients from the Gene Expression Omnibus(GEO)database(GSE151371).We identified 54 differentially expressed microRNAs and 1656 diffe rentially expressed genes using bioinformatics approaches.Functional enrichment analysis revealed that various common immune and inflammation-related signaling pathways,such as neutrophil extracellular trap formation pathway,T cell receptor signaling pathway,and nuclear factor-κB signal pathway,we re abnormally activated or inhibited in spinal cord inju ry patient samples.We applied an integrated strategy that combines weighted gene co-expression network analysis,LASSO logistic regression,and SVM-RFE algorithm and identified three biomarke rs associated with spinal cord injury:ANO10,BST1,and ZFP36L2.We verified the expression levels and diagnostic perfo rmance of these three genes in the original training dataset and clinical samples through the receiver operating characteristic curve.Quantitative polymerase chain reaction results showed that ANO20 and BST1 mRNA levels were increased and ZFP36L2 mRNA was decreased in the peripheral blood of spinal cord injury patients.We also constructed a small RNA-mRNA interaction network using Cytoscape.Additionally,we evaluated the proportion of 22 types of immune cells in the peripheral blood of spinal co rd injury patients using the CIBERSORT tool.The proportions of naive B cells,plasma cells,monocytes,and neutrophils were increased while the proportions of memory B cells,CD8^(+)T cells,resting natural killer cells,resting dendritic cells,and eosinophils were markedly decreased in spinal cord injury patients increased compared with healthy subjects,and ANO10,BST1 and ZFP26L2we re closely related to the proportion of certain immune cell types.The findings from this study provide new directions for the development of treatment strategies related to immune inflammation in spinal co rd inju ry and suggest that ANO10,BST2,and ZFP36L2 are potential biomarkers for spinal cord injury.The study was registe red in the Chinese Clinical Trial Registry(registration No.ChiCTR2200066985,December 12,2022).

Exploration of the efficacy and mechanism of treating head wind disease with the combination change of ginger volatile oil and gingerol by using content-weighted network pharmacology technology

Background:Exploring the efficacy,potential components,and mechanism of the combination of ginger essential oil and gingerols in the treatment of head wind disease based on network pharmacology technology with content weight.Methods:The experimental groups were divided into:0:10,1:4,1:2,1:1,2:1,4:1,10:0.The relative content(Ri)of the chemical constituents of ginger's volatile oil was determined using gas chromatography-mass spectrometry(GC-MS).Additionally,the physicochemical and biological property parameters(LogP,MDCK,PPB,MW)of the components were considered.To assess the quantitative effect of the components,a grading score was performed,and the quantitative effect index(Ki)was calculated.Subsequently,the target effect index(Ti)was calculated by combining the component-target matching score(Fit score).Using these calculations,the target effect score A was determined under the influence of multiple components targeting different targets.Key targets with A≥1000 were identified.To predict the targets related to head wind disease,the Comparative Toxicogenomics Database(https://ctdbase.org/),Gene Cards(https://www.genecards.org/),and Disgenet database(https://www.disgenet.org/)were utilized.The key targets,obtained from different proportions of ginger's volatile oil and gingerol,were intersected with the predicted targets.This facilitated network pharmacological analysis and verification of the efficacy.Results:The content of volatile oil in ginger demonstrated an impact on key targets associated with the volatile oil group.Each specific combination of volatile oil consistently activated distinct pathways,with variations stemming from changes in content.Experimental testing revealed that different combinations of ginger's volatile oil and gingerol effectively alleviated migraine symptoms in rats.Conclusion:Through the application of content-weighted network pharmacology technology and pharmacodynamic verification,it was determined that altering the ratio between ginger's volatile oil and gingerol leads to variations in potential targets and pathways,consequently impacting its efficacy.

Analysis of the COVID-19, Outbreak in Brazil Using Topological Weighted Centroid: An Intelligent Geographic Information System Approach

This study used Topological Weighted Centroid (TWC) to analyze the Coronavirus outbreak in Brazil. This analysis only uses latitude and longitude in formation of the capitals with the confirmed cases on May 24, 2020 to illustrate the usefulness of TWC though any date could have been used. There are three types of TWC analyses, each type having five associated algorithms that produce fifteen maps, TWC-Original, TWC-Frequency and TWC-Windowing. We focus on TWC-Original to illustrate our approach. The TWC method without using the transportation information predicts the network for COVID-19 outbreak that matches very well with the main radial transportation routes network in Brazil.

Longitudinal changes in body weight of breastfeeding mothers in the first year after delivery and its relationship with human milk composition:a combined longitudinal and cross-sectional cohort study

Objective:Postpartum weight retention(PPWR)is a common problem among women after childbirth.The main objectives of this study are to understand the changes in body weight of breastfeeding mothers during long-term follow-up and preliminarily explore the relationship between maternal body weight and human milk composition,including macronutrients,leptin,and adiponectin.Methods:The study included a longitudinal cohort(122 mothers),and a cross-sectional cohort(37 mothers).The human milk,maternal weight,and dietary surveys were collected in the longitudinal cohort at different follow-up time points(1-14 days postpartum,2-4 months postpartum,5-7 months postpartum,and 12-17 months postpartum).The maternal body weight was analyzed using the responses in the survey questionnaires.A milk analyzer based on the mid-infrared spectroscopy(MIRS)was used to determine milk composition,and nutrition analysis software evaluated dietary intakes.In the cross-sectional cohort,participating mothers were asked to provide blood and human milk samples and pertinent information related to maternal body composition.Maternal body composition was measured by bioelectrical impedance analysis(BIA),while ELISA analyzed leptin and adiponectin in milk and serum.Results:At 5-7 months postpartum,the PPWR of breastfeeding mothers was(2.46±3.59)kg.At 12-17 months postpartum,the PPWR was(0.98±4.06)kg.PPWR was found to be negatively correlated with milk fat content within 14 days postpartum and positively correlated at 2-4 months postpartum.In addition,the maternal weight and body muscle mass were positively correlated with leptin and adiponectin in milk.Plasma leptin was positively correlated with the mother’s body weight,body mass index(BMI),FAT percentage,and body fat mass,while plasma adiponectin did not correlate with any parameter.The results also indicate that the PPWR did not correlate with leptin and adiponectin in plasma or milk.Conclusions:Breastfeeding mothers may retain considerable weight gain one year after delivery.Human milk composition may be related to changes in maternal body weight.Leptin and adiponectin in breast milk and leptin in plasma are associated with the maternal body composition.This study supports the notion that maternal nutritional status may affect offspring health through lactation,and future research should focus on exploring weight management of postpartum mothers.

Effect of Molecular Weight on Thermoelectric Performance of P3HT Analogues with 2-Propoxyethyl Side Chains

By replacing hexyl chains in poly(3-hexylthiophene)(P3HT)with 2-propoxyethyls,four poly(3-(2-propoxyethyl)thiophene)(P3POET)homopolymers with comparable polydispersity indexes(PDI)and regioregularities were prepared herein in addition with step increment of about 7 kDa on numberaverage molecular weight(M_(n))from around 11 to 32 kDa(accordingly denoted as P11k,P18k,P25k,and P32k).When doped in film by FeCl_(3)at the optimized conditions,the maximum power factor(PF_(max))increases greatly from 4.3μW·m^(-1)·K^(-2)for P11k to 8.8μW·m^(-1)·K^(-2)for P18k,and further to 9.7μW·m^(-1)·K^(-2)for P25k,followed by a slight decrease to 9.2μW·m^(-1)·K^(-2)for P32k.The close Seebeck coefficients(S)at PF_(max)are observed in these doped polymer films due to their consistent frontier orbital energy levels and Fermi levels.The main contribution to this PF_(max)evolution thus comes from the corresponding conductivities(σ).Theσvariation of the doped films can be rationally correlated with their microstructure evolution.

A redundant subspace weighting procedure for clock ensemble

A redundant-subspace-weighting(RSW)-based approach is proposed to enhance the frequency stability on a time scale of a clock ensemble.In this method,multiple overlapping subspaces are constructed in the clock ensemble,and the weight of each clock in this ensemble is defined by using the spatial covariance matrix.The superimposition average of covariances in different subspaces reduces the correlations between clocks in the same laboratory to some extent.After optimizing the parameters of this weighting procedure,the frequency stabilities of virtual clock ensembles are significantly improved in most cases.

Spatial search weighting information contained in cell velocity distribution

Cell migration plays a significant role in physiological and pathological processes.Understanding the characteristics of cell movement is crucial for comprehending biological processes such as cell functionality,cell migration,and cell–cell interactions.One of the fundamental characteristics of cell movement is the specific distribution of cell speed,containing valuable information that still requires comprehensive understanding.This article investigates the distribution of mean velocities along cell trajectories,with a focus on optimizing the efficiency of cell food search in the context of the entire colony.We confirm that the specific velocity distribution in the experiments corresponds to an optimal search efficiency when spatial weighting is considered.The simulation results indicate that the distribution of average velocity does not align with the optimal search efficiency when employing average spatial weighting.However,when considering the distribution of central spatial weighting,the specific velocity distribution in the experiment is shown to correspond to the optimal search efficiency.Our simulations reveal that for any given distribution of average velocity,a specific central spatial weighting can be identified among the possible central spatial weighting that aligns with the optimal search strategy.Additionally,our work presents a method for determining the spatial weights embedded in the velocity distribution of cell movement.Our results have provided new avenues for further investigation of significant topics,such as relationship between cell behavior and environmental conditions throughout their evolutionary history,and how cells achieve collective cooperation through cell-cell communication.

Chemical modification of barite for improving the performance of weighting materials for water-based drilling fluids

With increasing drilling depth and large dosage of weighting materials,drilling fluids with high solid content are characterized by poor stability,high viscosity,large water loss,and thick mud cake,easier leading to reservoir damage and wellbore instability.In this paper,micronized barite(MB)was modified(mMB)by grafting with hydrophilic polymer onto the surface through the free radical polymerization to displace conventional API barite partly.The suspension stability of water-based drilling fluids(WBDFs)weighted with API barite:mMB=2:1 in 600 g was significantly enhanced compared with that with API barite/WBDFs,exhibiting the static sag factor within 0.54 and the whole stability index of 2.The viscosity and yield point reached the minimum,with a reduction of more than 40%compared with API barite only at the same density.Through multi-stage filling and dense accumulation of weighting materials and clays,filtration loss was decreased,mud cake quality was improved,and simultaneously it had great reservoir protection performance,and the permeability recovery rate reached 87%.In addition,it also effectively improved the lubricity of WBDFs.The sticking coefficient of mud cake was reduced by 53.4%,and the friction coefficient was 0.2603.Therefore,mMB can serve as a versatile additive to control the density,rheology,filtration,and stability of WBDFs weighted with API barite,thus regulating comprehensive performance and achieving reservoir protection capacity.This work opened up a new path for the productive drilling of extremely deep and intricate wells by providing an efficient method for managing the performance of high-density WBDFs.

Low Birth Weight and Intermittent Preventive Treatment of Malaria in Pregnant Women in Lomé (Togo) in 2021: A Cross-Sectional Study

Background: Since 2012, the World Health Organization has recommended intermittent preventive treatment with sulfadoxine-pyrimethamine (IPT-SP) to prevent malaria-related complications in pregnant women. Ten years following these recommendations, we conducted this study to estimate the coverage for three doses of IPT-SP (IPT3) as well as the prevalence of low birth weight (LBW), and its associated factors in Lomé (Togo) in 2021. Methods: A cross-sectional study was conducted between January and March 2021. An exhaustive recruitment of women and their newborns was carried out in the maternity wards of the Sylvanus Olympio University Hospital Center. Data from antenatal consultations and clinical data of the newborns were collected. Multivariate logistic regression was carried out to determine factors associated with LBW. Results: A total of 252 mother-child pairs were included in this study. Median age of the mothers was 27 years, IQR [24-31]. More than a third (35.3%) of the mothers were primigravida. IPT3 coverage was 66.7% and 14.7% of newborns had a LBW. The prevalence of LBW was 33.3% [23.3-43.4] in women who had received fewer than 3 doses of IPT-SP and 5.4% [2.0-8.8] in those who had received at least 3 doses of IPT-SP (p Conclusion: Ten years following recommendations of the WHO on IPT-SP, malaria prevention based on IPT-SP is not optimal among pregnant women in Lomé, and the proportion of LBW children remains high. Actions to strengthen the three-dose IPT-SP policy are needed to prevent malaria and its consequences among newborns in Togo.

Effects of low molecular weight polysaccharide from Sargassum thunbergii against palmitic acid-induced intracellular lipid accumulation in 3T3-L1 adipocyte and HepG2 cells

Low molecular weight polysaccharides can be isolated from Sargassum thunbergii(LMPST)and in vitro experiments were conducted to evaluate the inhibitory effects on lipids.Two natures of LMPST were attained from S.thunbergii and appraised their LMPST on palmitic acid(PA)induced lipid accretion in Hep G2,and 3T3-L1 cells.LMPST treatment lessened lipid deposition and intracellular free fatty acid and triglyceride intensities in PA-treated above mentioned cells.The mechanistic study publicized that LMPST2 significantly suppressed adipogenesis and stimulated the PA-treated 3T3-L1 cells occupied in the lipolysis pathway.Furthermore,in PA-treated Hep G2 cells,the free fatty acid oxidation was significantly increased by LMPST2.Given these constructive properties of LMPST2 from S.thunbergii,is a potential candidate for diminishing the intracellular lipids,and for a therapeutic agent in those conditions.