Standard Deviation Of Distance Research Articles

Abstract 17102: Establishing Outcome-Based Severity Partitions for LV Dilation

Background: The 2015 American Society of Echocardiography chamber quantification guideline 1 included healthy population-based normal controls for left ventricular (LV) size, but not severity partitions due to the lack of data to support mild, moderate, and severe categories. In this study, we propose using adverse outcomes to define “severe” in non-ischemic dilated cardiomyopathy (DCM). Methods: 778 adults with DCM were enrolled prospectively and underwent CMR from June 2012 to August 2020 at West China Hospital and followed for a median of 49 months 2 . 72 healthy Chinese adults served as controls. We evaluated “severe” increase in LV end-diastolic volume indexed to body surface area (EDVi), LVEDV/right ventricular (RV) EDV, and “severe” decrease in LV ejection fraction (EF) using receiver operator characteristic (ROC) and area under the curve (AUC) analysis based on cardiovascular outcome. We defined “moderate” as control mean +½ the standard deviation (SD) distance between control mean and “severe” and “mild” as between control mean +2 SD and “moderate”. Results: Of 778 participants, 190 experienced heart failure death, sudden cardiac death, or heart transplant. For LVEDVi, the “severe” dilation cut point was 184 mL/m 2 , 10.9 SD from control mean (71 ml/m 2 ). Thus, “moderate” dilation starts at 128 ml/m 2 (control mean +5.4 SD) and “mild” starts at 92 ml/m 2 (control mean +2 SD). The LVEDV/RVEDV ratio partitions are similar to RVEDV/LVEDV partitions for pulmonary arterial hypertension 3 . It is well known that LVEDVi and LVEF have sex-based differences with females having smaller hearts and higher EF 4 . the volume ratio is slightly lower in females as compared to the males (Table 1). Conclusion: Severity of LV dilation and dysfunction based on LVEDVi, LVEF, and LVEDV/RVEDV can be determined by finding upper limits of normal, using outcomes to determine “severe” category, and using the SD distance between severe and control mean to determine mild and moderate categories.

An Inter-observer Study to Determine Radiotherapy Planning Target Volumes for Recurrent Gynaecological Cancer Comparing Magnetic Resonance Imaging Only With Computed Tomography-Magnetic Resonance Imaging

AimsTarget delineation uncertainty is arguably the largest source of geometric uncertainty in radiotherapy. Several factors can affect it, including the imaging modality used for delineation. It is accounted for by applying safety margins to the target to produce a planning target volume (PTV), to which treatments are designed. To determine the margin, the delineation uncertainty is measured as the delineation error, and then a margin recipe used. However, there is no published evidence of such analysis for recurrent gynaecological cancers (RGC). The aims of this study were first to quantify the delineation uncertainty for RGC gross tumour volumes (GTVs) and to calculate the associated PTV margins and then to quantify the difference in GTV, delineation uncertainty and PTV margin, between a computed tomography-magnetic resonance imaging (CT-MRI) and MRI workflow. Materials and methodsSeven clinicians delineated the GTV for 20 RGC tumours on co-registered CT and MRI datasets (CT-MRI) and on MRI alone. The delineation error, the standard deviation of distances from each clinician's outline to a reference, was measured and the required PTV margin determined. Differences between using CT-MRI and MRI alone were assessed. ResultsThe overall delineation error and the resulting margin were 3.1 mm and 8.5 mm, respectively, for CT-MRI, reducing to 2.5 mm and 7.1 mm, respectively, for MRI alone. Delineation errors and therefore the theoretical margins, varied widely between patients. MRI tumour volumes were on average 15% smaller than CT-MRI tumour volumes. DiscussionThis study is the first to quantify delineation error for RGC tumours and to calculate the corresponding PTV margin. The determined margins were larger than those reported in the literature for similar patients, bringing into question both current margins and margin calculation methods. The wide variation in delineation error between these patients suggests that applying a single population-based margin may result in PTVs that are suboptimal for many. Finally, the reduced tumour volumes and safety margins suggest that patients with RGC may benefit from an MRI-only treatment workflow.

An Adaptive Density-Sensitive Similarity Measure Based Spectral Clustering Algorithm and Its Parallelization

The clustering effect of the spectral clustering algorithm depends on the calculation of the similarity between samples. Although a better clustering effect of the spectral clustering algorithm can be obtained using the Gaussian kernel function to calculate the similarity between samples, it relies on the setting of the kernel parameter. Therefore, an adaptive density-sensitive similarity measure based spectral clustering (DSSC) algorithm is proposed for improving the clustering effect. Specifically, firstly, the Euclidean distances between samples are calculated to get the nearest neighbors of each sample. Secondly, the standard deviation of distances between each sample and its nearest neighbors is calculated as the density parameter. Thirdly, the density-sensitive distances between each sample and its nearest neighbors are calculated. Finally, the similarities between each sample and its nearest neighbors are calculated to construct a similarity matrix. In addition, the proposed DSSC algorithm is parallelized on Dask distributed parallel computing platform with CPU+GPU, which can improve the computational efficiency of the DSSC algorithm by taking full advantage of the CPU and GPU resources. A series of experiments are conducted to verify the effectiveness of the proposed DSSC algorithm on several synthetic datasets and UCI datasets, and the results show that the DSSC algorithm not only achieves satisfactory clustering results, but also obtains better efficiency of performing large-scale clustering analysis.

Modelling of the reference STARs procedures in the context of RPAS integration in non-segregated airspace

PurposeThis work presents the part of the research in the integration of the remotely piloted aircraft systems (RPAS) in non-segregated airspace. The purpose of this study is to elaborate the reference shape of the Standard Instrument Arrivals (STARs) procedures of controlled airports. The STARs parameters are unique for the aerodromes and depend on navigational aids (NAVAIDs), manoeuvres and aircraft categories. Therefore, the elaboration of reference shapes was advisable in the context of RPAS integration research.Design/methodology/approachThe models were based on the procedure design guidelines by International Civil Aviation Organization. The statistics of existing STARs were prepared using Aeronautical Information Publications to determine the representative procedural parameters. Construction of procedural shapes required to define the nominal flight path and tolerance areas.FindingsIn statistics, the standard deviation of distances was below the determined reference mean values, thus the models were convergent with existing procedures.Research limitations/implicationsThe modelling was limited to initial, intermediate, final and missed approach segments. Arrival segment was not modelled. NAVAIDs include Instrument Landing System Category 1 (in final and missed approach) and very high-frequency omni-directional ranging or global navigation satellite systems (in initial and intermediate approach segments).Practical implicationsPrepared models may be used in research in the integration of the new types of aerial vehicles in existing air traffic management systems.Originality/valueThe reference STARs possess commonly used procedural manoeuvres (straight-in, turn, racetrack and base turn) and different NAVAIDs. The parameters of approach segments were determined as representative of the existing procedures. Moreover, the models are suitable to place at arbitrary origin and runway axis bearing.

Periodized Aerobic Interval Training Modifies Geometric Indices of Heart Rate Variability in Metabolic Syndrome.

Background: Metabolic syndrome (MetS) influences the autonomic modulation, increasing the risk of cardiovascular events, which demands the identification of effective treatments for this population. Considering this, the study has the objective of evaluating the effects of periodized aerobic interval training (AIT) on geometrical methods of heart rate variability (HRV) on individuals with MetS. Methods: 52 individuals with MetS were considered for analysis. They were divided into two groups: aerobic interval training group (AITG; n = 26) and control group (CG; n = 26). The AITG performed 16 weeks of periodized AIT. For HRV analysis, the heart rate was recorded beat-by-beat at the beginning and the end of the AIT program and geometrical methods were used for analysis. Results: significant increase was observed for triangular index (RRtri, −1.25 ± 0.58 vs. 1.41 ± 0.57), standard deviation of distances from diagonal to points (SD1, −0.13 ± 1.52 vs. 4.34 ± 1.49), and standard deviation of distances from points to lines (SD2, −2.14 ± 3.59 vs. 11.23 ± 3.52) on AITG compared to CG. Significant differences were not observed for triangular interpolation of normal heartbeats interval histogram (TINN, −4.05 ± 17.38 vs. 25.52 ± 17.03) and SD1/SD2 ratio (0.03 ± 0.02 vs. 0.00 ± 0.02). Qualitative analysis of the Poincaré plot identified increase on dispersion of both short and long-term intervals between successive heartbeats (RR interval) on AITG after the AIT program. Conclusion: geometric indices of HRV suggest an increase in cardiac autonomic modulation in individuals with MetS after 16 weeks of periodized AIT.

Human behaviour in the Euclidean Travelling Salesperson Problem: Computational modelling of heuristics and figural effects

The Travelling Salesperson Problem (TSP) describes a situation where an imaginary individual wishes to visit multiple cities once before returning to his/her own city. This type of problem is known as a nondeterministic polynomial (NP) hard problem, since the factorial number of solutions results in it being impractical to solve using exhaustive processing. Interestingly, when presented as a Euclidean graph (i.e., ETSP), humans identify near optimal solutions almost effortlessly, despite billions of possible tours. In this study, we consider human processing of the ETSP, and introduce the reader to a number of factors that literature proposes as impacting human performance. We hypothesise that: (i) human ETSP activity may be modelled by considering the quotient relationship between node-to-node and node-to-centroid distances; and (ii) consideration of figural effects can optimise automated TSP solution generation. In this paper human processing based heuristics are developed, i.e. replacing the cost function within the nearest neighbour algorithm, to guide node selection. Results showed that the quotient relationship between node-to-node and node-to-centroid distances can be used to closely model average human performance, across a range of ETSP graphs. Interestingly, however, additional consideration of graph figural effects (e.g. distance between boundary points in the convex hull, standard deviation of distances between nodes that make up the convex hull, and number of nodes in the convex hull) results in significantly improved tour costs.

Classic high lateral tension and triangular resection methods to prevent dog ear and elongation scar in patients undergoing abdominoplasty: A comparative open-label clinical trial.

Background:One of the most common operations in the plastic surgery curse is abdominoplasty. Several methods were recommended for achieving better results. In the present study, efficacy of a new method compared with classical high lateral tension on preventing dog ear and elongation scar was evaluated.Materials and Methods:in an open-label, randomized clinical trial, seventy patients who were candidates for abdominoplasty were selected and randomly divided into two groups. The first group was operated by classic high lateral method and the second group was operated by a new method concentrating on changing incision line and angle. Dog ear prevention, length of scar, improvement, and postoperative complications were compared between the two groups.Results:The mean ± standard deviation (SD) length of scar in treated patients with classical and new abdominoplasty surgical methods was 53.68 ± 6.34 and 41.71 ± 1.78 cm, respectively, and the length of scar in the group treated with the new method was significantly shorter (P < 0.001). The mean ± SD distance between two anterior superior iliac spine in group treated by new method was significantly decreased after surgery (31.3 ± 1.3 cm) compared to before intervention (36.7 ± 3.9 cm) (P < 0.01).Conclusion:The new method is more likely to be successful in patients with high lateral tension abdominoplasty. However, according to the lack of similar studies in this regard and the fact that this method was introduced for the first time, it is recommended that further studies in this area are needed and patients in term of complications after surgery need a longer period of follow-up.

단일 2차원 라이다 기반의 다중 특징 비교를 이용한 장애물 분류 기법

We propose an obstacle classification method using multi-decision factors and decision sections based on Single 2D LiDAR. The existing obstacle classification method based on single 2D LiDAR has two specific advantages: accuracy and decreased calculation time. However, it was difficult to classify obstacle type, and therefore accurate path planning was not possible. To overcome this problem, a method of classifying obstacle type based on width data was proposed. However, width data was not sufficient to enable accurate obstacle classification. The proposed algorithm of this paper involves the comparison between decision factor and decision section to classify obstacle type. Decision factor and decision section was determined using width, standard deviation of distance, average normalized intensity, and standard deviation of normalized intensity data. Experiments using a real autonomous vehicle in a real environment showed that calculation time decreased in comparison with 2D LiDAR-based method, thus demonstrating the possibility of obstacle type classification using single 2D LiDAR.

Does travel distance influence length of stay in elective pancreatic surgery?

BackgroundLength of stay (LoS) following elective surgery is being reported as an outcomes quality measure. Regional referral centres may care for patients travelling significant distances. The effect of travel distance on LoS in pancreatic surgery patients was examined. MethodsNational Surgical Quality Improvement Program data on pancreatic surgery patients, operated during the period from 2005 to 2011, were reviewed. Demographics, surgical variables and distance travelled were analysed relative to LoS. The LoS was log-transformed in general linear models to achieve normality. ResultsOf the 243 patients, 53% were male. The mean ± standard deviation (SD) age of the total patient sample was 60.6 ± 14 years. The mean ± SD distance travelled was 203 ± 319 miles (326.7 ± 513.4km) [median: 132 miles (212.4km); range: 3–3006 miles (4.8–4837.7km)], and the mean ± SD LoS was 10.5 ± 7 days (range: 1–46 days). Univariate analysis showed a near significant increase in LoS with increased distance travelled (P = 0.05). Significant variables related to LoS were: age (P = 0.002); relative value units (P < 0.001), and preoperative American Society of Anesthesiologists class (P = 0.005). In a general linear model, for every 100 miles (160.9km) travelled there is an associated 2% increase in LoS (P = 0.031). When the distance travelled is increased by 500 miles (804.7km), LoS increases by 10.5%. ConclusionsIncreased travel distance from a patient's home to the hospital was independently associated with an increase in LoS. If LoS is a reportable quality measure in pancreatic surgery, travel distance should be considered in risk adjustments.

Comparison of the Therapeutic and Side Effects of Tadalafil and Sildenafil in Children and Adolescents with Pulmonary Arterial Hypertension

Pulmonary arterial hypertension (PAH) is a progressive disease. In recent years, phosphodiesterase type 5 inhibitors such as sildenafil have been used to treat this disease in children. Recently, tadalafil has been used in adults with similar efficacy but it has been used less often in children. This experimental study was carried out in 18 known patients aged 4-24 years in the Emam Hossein Hospital of Isfahan, Iran. All patients had been taking sildenafil for a few months to years. Patients underwent echocardiographic study, the 6-minute walk test (6MWT), and non-invasive pulse oximetry before and after the 6MWT. These tests were repeated again after sildenafil had been switched to tadalafil for 6 weeks. After 6 weeks of tadalafil prescription, the severity of some of the patients' symptoms decreased, but the New York Heart Association class of the patients did not change more. Mean ± standard deviation (SD) oxygen saturation while taking sildenafil and after 6 weeks of tadalafil were significantly different (p = 0.005). Furthermore, mean ± SD oxygen saturation after the 6MWT while taking sildenafil and after 6 weeks of tadalafil were significantly different (p = 0.036). The mean ± SD distances walked in this test while taking sildenafil and tadalafil were significantly different (p = 0.005). No significant side effects were seen; 15 patients continued tadalafil. Tadalafil may be a safe drug to treat children and young adults with PAH. We did not observe any significant side effects during usage; it improves functional capacity and oxygen saturation better than sildenafil in these patients, and requires fewer daily doses than sildenafil.

주차보조를 위한 초음파 센서 기반의 주변차량의 주차상태 및 기둥 분류

This paper proposes a classification method of parallel, vertical parking states and pillars for parking assist system using ultrasonic sensors. Since, in general parking space detection module, the compressed amplitude of ultrasonic data are received, the analysis of them is difficult. To solve these problems, in preprocessing state, symmetric transform and noise removal are performed. In feature extraction process, four features, standard deviation of distance, reconstructed peak, standard deviation of reconstructed signal and sum of width, are proposed. Gaussian fitting model is used to reconstruct saturated peak signal and discriminability of each feature is measured. To find the best combination among these features, multi-class SVM and subset generator are used for more accurate and robust classification. The proposed method shows 92 % classification rate and proves the applicability to parking space detection modules.

A revised automated proximity and conformity analysis method to compare predicted and observed spatial boundaries of geologic phenomena

Quantitative assessment of the level of agreement between model-predicted and field-observed geologic data is crucial to calibrate and validate numerical landscape models. Application of Geographic Information Systems (GIS) provides an opportunity to integrate model and field data and quantify their levels of correspondence. Napieralski et al. [Comparing predicted and observed spatial boundaries of geologic phenomena: Automated Proximity and Conformity Analysis (APCA) applied to ice sheet reconstructions. Computers and Geosciences 32, 124–134] introduced an Automated Proximity and Conformity Analysis (APCA) method to compare model-predicted and field-observed spatial boundaries and used it to quantify the level of correspondence between predicted ice margins from ice sheet models and field observations from end moraines. However, as originally formulated, APCA involves a relatively large amount of user intervention during the analysis and results in an index to quantify the level of correspondence that lacks direct statistical meaning. Here, we propose a revised APCA approach and a more automated and statistically robust way to quantify the level of correspondence between model predictions and field observations. Specifically, the mean and standard deviation of distances between model and field boundaries are used to quantify proximity and conformity, respectively. An illustration of the revised method comparing modeled ice margins of the Fennoscandian Ice Sheet with observed end moraines of the Last Glacial Maximum shows that this approach provides a more automated and statistically robust means to quantify correspondence than the original APCA. The revised approach can be adopted for a wide range of geoscience issues where comparisons of model-predicted and field-observed spatial boundaries are useful, including mass movement and flood extents.

Positional Stability of Electromagnetic Transponders Used for Prostate Localization and Continuous, Real-Time Tracking

To determine the relative positional stability of implanted glass-encapsulated circuits (transponders) used in continuous electromagnetic localization and tracking of target volumes during radiation therapy. Ideally, the distances between transponders remains constant over the course of treatment. In this work, we evaluate the accuracy of these conditions. Three transponders were implanted in each of 20 patients. Images (CT scan or X-ray pair) were acquired at 13 time points. These images occurred from the day of implant (2 weeks before simulation) to 4 weeks posttreatment. The distance between transponders was determined from each dataset. The average and standard deviation of each distance were determined, and changes were evaluated over several time periods, including pretreatment and during therapy. Of 60 transponders implanted, 58 showed no significant migration from their intended positions. Of the two transponders that did migrate, one appears to have been implanted in the venous plexus, and the other in the urethra, with no clinical consequences to the patients. An analysis that included the planning CT scan and all subsequent distance measurements showed that the standard deviation of intertransponder distances was < or =1.2 mm for up to 1 month after the completion of therapy. Implanted transponders demonstrate the same long-term stability characteristics as implanted gold markers, within statistical uncertainties. As with gold markers, and using the same implant procedure, basic guidelines for the placement of transponders within the prostate help ensure minimal migration.

Evaluation of cortical current density imaging methods using intracranial electrocorticograms and functional MRI

Objective:EEG source imaging provides important information regarding the underlying neural activity from noninvasive electrophysiological measurements. The aim of the present study was to evaluate source reconstruction techniques by means of the intracranial electrocorticograms (ECoGs) and functional MRI. Methods:Five source imaging algorithms, including the minimum norm least square (MNLS), LORETA with Lp-norm (p equal to 1, 1.5 and 2), sLORETA, the minimum Lp-norm (p equal to 1 and 1.5; when p=2, the MNLS method is mathematically equivalent to the minimum Lp-norm) and L1-norm (the linear programming) methods, were evaluated in a group of 10 human subjects, in a paradigm with somatosensory stimulation. Cortical current density (CCD) distributions were estimated from the scalp somatosensory evoked potentials (SEPs), at approximately 30 ms following electrical stimulation of median nerve at the wrist. Realistic geometry boundary element head models were constructed from the MRIs of each subject and used in the CCD analysis. Functional MRI results obtained from a motor task and sensory stimulation in all subjects were used to identify the central sulcus, motor and sensory areas. In three patients undergoing neurosurgical evaluation, ECoGs were recorded in response to the somatosensory stimulation, and were used to help determine the central sulcus and the sensory cortex. Results:The CCD distributions estimated by the Lp-norm and LORETA-Lp methods were smoother when the p values were high. The LORETA based on the L1-norm performed better than the LORETA-L2 method for imaging well localized sources such as the P30 component of the SEP. The mean and standard deviation of the distance between the location of maximum CCD value and the central sulcus, estimated by the minimum Lp-norm (with p equal to 1), L1-norm (the Linear programming) and LORETA-Lp (with p equal to 1) methods, were 4, 7, 7 mm and 3, 4, 2 mm, respectively (after converting into Talairach coordinates). The mean and standard deviation of the aforementioned distance, estimated by the MNLS, LORETA with Lp-norm (p equal to 1.5 and 2.0), sLORETA and the minimum Lp-norm (p equal to 1.5) methods, were over 11 mm and 6 mm, respectively. Conclusions:The present experimental study suggests that L1-norm-based algorithms provide better performance than L2 and L1.5-norm-based algorithms, in the context of CCD imaging of well localized sources induced by somatosensory electrical stimulation of median nerve at the wrist.

New gene selection method for classification of cancer subtypes considering within-class variation

In this work we propose a new method for finding gene subsets of microarray data that effectively discriminates subtypes of disease. We developed a new criterion for measuring the relevance of individual genes by using mean and standard deviation of distances from each sample to the class centroid in order to treat the well-known problem of gene selection, large within-class variation. Also this approach has the advantage that it is applicable not only to binary classification but also to multiple classification problems. We demonstrated the performance of the method by applying it to the publicly available microarray datasets, leukemia (two classes) and small round blue cell tumors (four classes). The proposed method provides a very small number of genes compared with the previous methods without loss of discriminating power and thus it can effectively facilitate further biological and clinical researches.

Spacing of fetuses and local competition in strains of mice with large, medium and small litters.

The tendency for fetuses to be evenly spaced along the uterine horn and the relationship of this to local competition between fetuses was examined in three strains of mice which characteristically produce large, medium and small litters. Local competition was assessed by correlating, within each uterine horn, the weight of each fetus or placenta with the mean distance to its immediate neighbours. Weights and distances were measured on day 19 of gestation, on the day before expected parturition and distances only on day 7. Average litter sizes (live fetuses) were 16.3 +/- 0.9, 11.7 +/- 0.6 and 7.2 +/- 0.5 (mean +/- SEM) in the large, medium and small litter strains, respectively (n = 7, 7 and 10, respectively). On day 19, the mean distance between fetuses was significantly less (P < 0.05) in the large strain (10.1 +/- 1.0 mm) than in the medium (14.0 +/- 1.2 mm) or small (13.5 +/- 1.0 mm) strains. Evenness of spacing, expressed as the standard deviation of distances between fetuses divided by the mean distance, improved from day 7 to day 19 of gestation in all three strains and effectively prevented local competition between fetuses in the medium litter (r = 0.04) and small litter strains (r = 0.17), but not in the large litter strain (r = 0.45, P < 0.01). Thus, local crowding does not seem to be detrimental to fetal growth in mice, except in strains specifically bred for large litters.

Feasibility Studies on Planting Corn Trials to a Stand1

Researchers have historically stressed uniformity of plant stands in corn (Zea mays L.) yield trials to reduce variability. This has mandated that all trials be over‐planted and later thinned. For this study, field trials were conducted in seven environments to determine the feasibility of planting corn yield trials to a stand by planting at a seeding rate of 110% of desired stand; this was compared to the standard practice of overplanting and thinning. Ten hybrids in each of three maturity groups were randomly selected for the study. A split plot arrangement was used with whole plots consisting of hybrids and subplots consisting of thinning vs. no‐thinning of stands. Soil types were a Portsmouth sandy loam (fine‐loamy over sandy or sandy‐skeletal, mixed, thermic Typic Umbraquults) and a Goldsboro loamy sand (fine‐loamy siliceous, thermic Aquic Paleudults). Variables analyzed included yield, percentage of desired stand, and standard deviation of distance between adjacent plants. Planting to a stand (no‐thin) resulted in less uniform stands for all maturity groups; however, this did not produce significantly lower yields. Percentage of desired stand was equivalent between the two treatments for early and medium‐maturing hybrids but the no‐thin treatment produced significantly greater than 100% stands for the late‐maturing hybrids. Error variances and F values for analyzing yield among entries were comparable between the two treatments. Nonsignificant entry‐treatment and environment‐entry‐treatment interactions and equivalent stands suggest that planting to a stand is feasible.

The Intelligence Factor in Foreign-Language Achievement

Recent investigations of the correlation between intelligence and success in foreign-language study have yielded somewhat optimistic conclusions concerning the value of the intelligence quotient in predicting achievement. That this optimism is not wholly justified is evident from the results of the investigation reported in this article, which is probably the most comprehensive study of the intelligence factor in foreign-language achievement thus far reported. The materials of the study, which was made during the second semester of the school year 1927-28, are the intelligence quotients of 1,002 pupils, derived from their performance on the Terman Group Test of Mental Ability, Forms A and B, and certain of their marks in Spanish. The pupils, who were enrolled in eighteen junior and senior high schools in San Diego and Los Angeles, had studied Spanish from one to six semesters. The marks in Spanish for the last two semesters of study were averaged for all except beginning pupils. These averages were translated into point-score equivalents on the basis of their standard-deviation distances on the linear scale