Midpoint Of Interval Research Articles

Towards quantifying uncertainties in geological models for mineral resource estimation through outside-in deposit-scale structural geological analysis

Mineral Resource downgrades can be prevented by integrating better structural geological interpretations into project evaluations. Geological modelling for Mineral Resource estimation is presented as a systematic process of structural geological analysis at the deposit-scale using drill-sampled grade data. The initial step in this process is to use Maximum Intensity Projection (MIP) rendering to interpret axial symmetry and its orientation from the grade interval mid-points at the deposit-scale, thus reducing the modelling process’s degrees of freedom to only three—estimating the prolateness of the grade or lithological distribution. This approach contrasts with the brute-force methods for assessing modelling uncertainty because the axial direction is fixed to the down-plunge orientation, thus eliminating from the outset, structurally implausible geometric configurations and unrealistic geological scenarios common in brute-force methods. Adopting this new approach of creating geological models means moving away from conventional mining industry methods that prioritise operational considerations in constructing resource estimates but fail to explain the geometric complexities of mineral deposits. We use experiments and a practical case study of a historical gold mine in Western Australia to highlight the significance of analysing the structural control of a gold deposit at the deposit-scale using raw grade data. Our research is based on anecdotal evidence suggesting that erroneous geological modelling leads to unforeseen Mineral Resource downgrades. However, we cannot confirm this hypothesis because there have been few, if any, independent public inquiries into Mineral Resource downgrades. To establish the underlying reasons for significant resource downgrades with certainty, impartial investigations (modelled on accident investigations in the aviation industry) are imperative.

Differential effects of chronotype on physical activity and cognitive performance in older adults.

Chronotypes reflect individuals' preferred activity and sleep patterns (e.g., "morning-types" vs. "evening-types") and are associated with health and physical activity. Less is known about the relationship between chronotype and cognitive health in older adults. It is unclear whether chronotype's influence is driven by sleep timing or disruption. This study explored the relationship between chronotype, physical activity, and cognitive performance in older adults with and without self-reported sleep disorders. Participants were 153 older adults (M = 70.35, SD = 5.89) who wore an Actigraph on the non-dominant wrist for seven days to measure total physical activity, peak physical activity, and chronotype (sleep interval midpoint). We categorized participants as morning-, evening-, and intermediate-chronotypes and assessed cognitive performance in domains of attention, executive function, and verbal memory. MANCOVAs showed patterns of activity across the 24-hour day differed between chronotypes such that morning-types were active earlier and evening-types active later, ps > .001. Total physical activity and average peak activity did not differ between chronotypes, (ps ≥ .117). Timing of peak activity followed expectations (morning-types peaked earliest (p = .019). Evening-types exhibited significantly worse executive function and attention than intermediate-types, p = .008. When excluding participants with sleep disorders, evening-types engaged in significantly less total physical activity than other groups, but cognitive performance did not differ. We found no differences in total or peak physical activity between groups, which is inconsistent with findings from studies in younger samples. This suggests the role of chronotype on physical activity may change with age and points to the potential impact of methodological discrepancies. While evening-types exhibited worse executive function and attention performance, this finding disappeared when participants with sleep disorders were excluded. Sleep dysregulation rather than sleep timing may be driving this difference. Recent trends in physical activity research explore activity patterns across the 24-hour day and acknowledge codependence between different activity types. Our findings suggest chronotype and activity timing may be important as researchers advance this line of research in older adults.

Global path planning method for smart driving cars based on extension neural network

Current global path planning algorithms for smart driving cars are capable of effective path type output, but some of them are expensive to develop and are not conducive to maintenance and iteration. In this paper, based on an extension neural network (ENN), the basic-elements model in Extenics is used to construct the information-elements involved in global path planning for smart driving cars as the input of the neurons; the maximum and minimum values of the quantity values of the input information-elements are used as the double weight values, and the midpoint of the interval formed by them is used as the midpoint of weight value interval, and the initial output function of the extension neurons is constructed based on the midpoint extension distance; The input and output layers are connected by double weight values to build the overall structure of the ENN for global path planning of smart driving cars. The ENN model is trained by collecting relevant data, adjusting the weight values and midpoints of weight value intervals of the ENN for incorrect predictions, and replacing the initial weight values and midpoints of weight value intervals to form a new output function. The trained model can predict path types quickly and accurately, showing that ENN can be used to optimize the efficiency and accuracy of the global path planning algorithm for smart driving cars in terms of output path types.

Self-selected interval judgments compared to point judgments: A weight judgment experiment in the presence of the size-weight illusion.

Measurements of human attitudes and perceptions have traditionally used numerical point judgments. In the present study, we compared conventional point estimates of weight with an interval judgment method. Participants were allowed to make step by step judgments, successively converging towards their best estimate. Participants estimated, in grams, the weight of differently sized boxes, estimates thus susceptible to the size-weight illusion. The illusion makes the smaller of two objects of the same weight, differing only in size, to be perceived as heavier. The self-selected interval method entails participants judging a highest and lowest reasonable value for the true weight. This is followed by a splitting procedure, consecutive choices of selecting the upper or lower half of the interval the individual estimates most likely to include the true value. Compared to point estimates, interval midpoints showed less variability and reduced the size-weight illusion, but only to a limited extent. Accuracy improvements from the interval method were limited, but the between participant variation suggests that the method has merit.

Applying Set Membership Strategy in State of Charge Estimation for Lithium-ion Battery

As state of charge is one important variable to monitor the later battery management system, and as traditional Kalman filter can be used to estimate the state of charge for Lithium-ion battery on basis of probability distribution on external noise. To relax this strict assumption on external noise, set membership strategy is proposed to achieve our goal in case of unknown but bounded noise. External noise with unknown but bounded is more realistic than white noise. After equivalent circuit model is used to describe the Lithium-ion battery charging and discharging properties, one state space equation is constructed to regard state of charge as its state variable. Based on state space model about state of charge, two kinds of set membership strategies are put forth to achieve the state estimation, which corresponds to state of charge estimation. Due to external noise is bounded, i.e. external noise is in a set, we construct interval and ellipsoid estimation for state estimation respectively in case of external noise is assumed in an interval or ellipsoid. Then midpoint of interval or center of the ellipsoid are chosen as the final value for state of charge estimation. Finally, one simulation example confirms our theoretical results.

A modified affine arithmetic-based interval optimization for integrated energy system with multiple uncertainties

In integrated energy systems, uncertainties cause day-ahead scheduling plans to be uncertain rather than an exact solution. However, traditional interval optimization models ignore the correlation between variables, resulting in an over-conservative range of solutions. To overcome this limitation, the present paper proposes a modified affine arithmetic to establish an interval optimal scheduling model based on deterministic optimization. The correlation between different variables is tracked by sharing noise terms, and the solution in affine form is transformed into a more intuitive interval solution by a modified affine approximation method and linear relaxation method. Finally, with the minimum midpoint and radii of daily operating cost interval as the objective function, the multi-objective function is converted into a single-objective function through Lagrange multiplication to solve the model. In a case study, the proposed method is compared with the Monte Carlo simulation method and the traditional interval optimization method without affine arithmetic. The simulation results show that the radii of the interval solutions obtained by the proposed method is 9.39% less than the traditional interval arithmetic at the 15% level of uncertainty.

Extreme Learning Machine based Pattern Classifiers for Symbolic Interval Data

Interval data are usually applied where inaccuracy and variability must be considered. This paper presents a learning method for Interval Extreme Learning Machine (IELM) in classification. IELM has two steps similar to well known ELM. At first weights connecting the input and the hidden layers are generated randomly and in the second step, ELM uses the Moore–Penrose generalized inverse to determine the weights connecting the hidden and output layers. In order to use Moore–Penrose generalized inverse for determining second layer weights in IELM, this paper proposes four classification methods to handle symbolic interval data based on ELM. The first one uses a midpoint of intervals for each feature value then it applies a classic ELM. The second one considers each feature value as a pair of quantitative features and implements a conjoint for classic extreme learning machine. The third one represents interval features by their vertices and performs a classic extreme learning machine as well. The fourth one takes each interval as a pair of quantitative features after that two separated classic extreme learning machines are performed on these features and combines the results accordingly. Algorithms are tested on the synthetic and real datasets. A synthetic dataset is applied to determine the number of hidden layer nodes in an IELM. The classification error rate is considered as a comparison criterion. The error rate obtained for each proposed methods is 19.1667%, 15% , 6.5358% and 18.3333% respectively. Experiments demonstrate the usefulness of these classifiers to classify symbolic interval data.

Regression with interval-censored covariates: Application to cross-sectional incidence estimation.

A method for generalized linear regression with interval-censored covariates is described, extending previous approaches. A scenario is considered in which an interval-censored covariate of interest is defined as a function of other variables. Instead of directly modeling the distribution of the interval-censored covariate of interest, the distributions of the variables which determine that covariate are modeled, and the distribution of the covariate of interest is inferred indirectly. This approach leads to an estimation procedure using the Expectation-Maximization (EM) algorithm. The performance of this approach is compared to two alternative approaches, one in which the censoring interval midpoints are used as estimates of the censored covariate values, and another in which the censored values are multiply imputed using uniform distributions over the censoring intervals. A simulation framework is constructed to assess these methods' accuracies across a range of scenarios. The proposed approach is found to have less bias than midpoint analysis and uniform imputation, at the cost of small increases in standard error.

Simulation of the eigenvalue problem for tapered rotating beams by the modified decomposition method

The modified decomposition method is applied to analyze the transverse vibrations of tapered rotating beams incorporating both axial centrifugal stiffening and flexible end constraints. Unlike prior analyses relying upon a power series expansion about the left end constraint, we instead expand the solution for the transverse deflection about the interval midpoint, which has significant advantages including an increased rate of convergence and readily adaptation to the Robin-type boundary conditions. The modified decomposition method facilitates systematic solution of the mathematical model including parametric simulations where the boundary conditions can be varied without resolving the original equation.

Neglect in temporal domain: Amelioration following a prismatic adaptation treatment and implications in everyday life. A single case study

As in line bisection, in time bisection, neglect patients fail to process the first/left part of time representation (Mental-Time-Line-MTL) resulting in a rightward shift of the interval midpoint. A leftward shift of spatial attention after one session of prismatic-adaptation (PA) reduces this deficit. The impact on daily life of time deficit is little investigated in neglect. Here we study the time deficit and its ecological impact in an outpatient with neglect (LL) and the effects of a PA-treatment (ten sessions) on the deficit and its impact.Before and after PA-treatment, LL completed a: time-bisection-task assessing the MTL in the milliseconds-seconds range; lifespan-task assessing the MTL in the lifespan range; qualitative interview assessing the impact on daily routines. Patient’s performance on the tasks was compared with the performance of non-neurological controls.Before PA-treatment, LL showed a rightward shift in the time-bisection-task and a compression of life events distribution in the lifespan-task. The feeling “to be forward in time” emerged in the interview. The PA-treatment reduced the deficits in the tasks and the feeling “to be forward in time” in the interview. PA-treatment is suggested as a powerful instrument for the reduction of time deficit and its ecological impact in neglect patients.

OR29-01 Long-Term Safety in Adults with X-Linked Hypophosphatemia (XLH) Treated with Burosumab, a Fully Human Monoclonal Antibody Against FGF23: Final Results of a Phase 3 Trial

Burosumab, a fully human IgG1 monoclonal antibody to FGF23, is approved in Canada and Brazil to treat XLH in patients ≥1 year of age and in the US to treat XLH in patients ≥6 months of age. Burosumab has also received conditional marketing authorization in Europe to treat XLH with radiographic evidence of bone disease in children ≥1 year of age and in adolescents with growing skeletons. Burosumab significantly improved serum phosphorus, fracture/pseudofracture healing, stiffness, and physical functioning in a phase 3, double-blind, multicenter study (CL303, NCT02526160). In this trial, subjects were randomized 1:1 to receive burosumab or placebo subcutaneously every 4 weeks. At Week 24, subjects in the placebo group crossed over to receive burosumab (total duration ≥96 weeks). Here, we report final long-term safety results from this trial. Most (119/134, 89%) subjects completed 96 weeks and received 1 mg/kg burosumab; protocol-specified dose reductions were required for 11/134 (8.2%) subjects to effectively manage hyperphosphatemia (all mild [Grade 1]). Mean (±SE) baseline serum phosphorus was 1.98 (±0.03) mg/dL and was 2.97 (±0.05) mg/dL at Week 94 (midpoint of dose interval). Mean (±SE) iPTH level was 96 (±3.8) pg/mL at baseline and progressively declined to 79 (±3.3) pg/mL at Week 96. Nephrocalcinosis score at Week 96 changed by 0 in 101 subjects, -1 in 9 subjects, +1 in 10 subjects (14 subjects not available). There were no meaningful changes in ectopic mineralization. There were no neutralizing antibodies. No treatment-emergent adverse events led to study or treatment withdrawal. Serum phosphorus was maintained with long-term burosumab treatment, with no evidence of loss of effect in adults with XLH. Burosumab dose reductions effectively managed mild hyperphosphatemia. Frequency, severity, and types of AEs reported were consistent with previous burosumab trials.

Second Order Pressure Estimates for the Crank--Nicolson Discretization of the Incompressible Navier--Stokes Equations

We provide optimal order pressure error estimates for the Crank--Nicolson semidiscretization of the incompressible Navier--Stokes equations. Second order estimates for the velocity error are long known; we prove that the pressure error is of the same order if considered at interval midpoints, confirming previous numerical evidence. For simplicity we first give a proof under high regularity assumptions that include nonlocal compatibility conditions for the initial data, then use smoothing techniques for a proof under reduced assumptions based on standard local conditions only.

Does midlife aging impact women's sleep duration, continuity, and timing?: A longitudinal analysis from the Study of Women's Health Across the Nation.

Our study objectives were to evaluate the age-related changes in actigraphy measures of sleep duration, continuity, and timing across 12 years in midlife women as they traversed the menopause, and to take into account factors affecting women's sleep that also change with age. Black, white, and Chinese women were recruited from the Study of Women's Health Across the Nation (SWAN) to participate in an ancillary sleep study on two occasions over 3 years apart and a third assessment 12 years after the first (N = 300, mean ages, 52, 55, and 64 at the three assessments). Women had at least four consecutive nights of actigraphy (95% with 7 nights) and sleep diaries, and self-reported sleep complaints measured at each time point. Partial correlations adjusted for time between assessments across the 12 years were significant and moderate in size (r's = .33-.58). PROC MIXED/GLIMMIX multivariate models showed that sleep duration increased over time; wake after sleep onset (WASO) declined, midpoint of sleep interval increased, and sleep latency and number of sleep complaints did not change between the first and third assessments. Blacks and whites had a greater increase in sleep duration than Chinese. Taken together, the results of this longitudinal study suggest that sleep may not worsen, in general, in midlife women. Perhaps, the expected negative effect of aging in midlife into early old age on sleep is overstated.

The Number Interval Position Effect (NIPE) in the mental bisection of numerical intervals might reflect the influence of the decimal-number system on the Gaussian representations of numerosities: A combined developmental and computational-modeling study

Healthy adults show typical error biases when they mentally bisect number intervals without exact calculations. For a given number interval length, the bisection bias is in fact modulated by the position that the interval occupies within a ten. For intervals positioned at the beginning of tens the error bias is directed toward values that are higher than those of the true interval midpoint whereas for intervals at the end of tens the direction of the error bias is reversed toward values that are lower than that of the true midpoint (Doricchi et al., 2009; Rotondaro et al., 2015). This effect has been defined Number Interval Position Effect (NIPE). The NIPE recurs over consecutive tens and it is not found when intervals are bisected through exact calculations. For this reasons we have hypothesized that the NIPE reflects the influence that the habit of counting in tens has on the neural representations of numerosities that humans share with other species. Here, in a developmental study we demonstrate that children from preschool to fifth-grade display a NIPE that is comparable to that of healthy adults. Then, through a computational-modeling study we investigated whether the NIPE might reflect specific patterns in the Gaussian representations of numerosities that are found in the parietal and pre-frontal neuronal populations of macaque monkeys and that underlie approximate numerosity estimations also in humans. The findings of computational simulations suggest that the NIPE might reflect the influence that the learning and use of the decimal numerical system has on the phylogenetically and ontogenetically older representation of numerosities that humans share with other species. These changes in the representation of numerosities have an influence on approximate numerical estimations even when these, like in the case of the mental bisection of number intervals, are elicited by numerical symbols or words.

Comparing the magnitude of fuzzy intervals and fuzzy random variables from the standpoint of gradual numbers

Gradual numbers have been introduced to separate fuzziness (understood as gradation) from uncertainty in so-called fuzzy numbers. Then a fuzzy number can be viewed as a standard interval of functions, each interpreted as a gradual number. Gradual numbers are naturally met when representing probabilities of fuzzy events, midpoints of fuzzy intervals, etc. They can be viewed as a non-monotonic generalization of cumulative probability distributions. This paper presents three methods for comparing gradual numbers that generalize stochastic orderings to such non-monotonic functions. Then it proposes joint extensions of stochastic dominance and statistical preference to random fuzzy intervals when the fuzzy intervals are understood as intervals of gradual numbers. This approach, which combines known probabilistic orderings with known forms of interval orderings, can be viewed as a systematic way of constructing methods for ranking fuzzy random variables.

Daytime midpoint as a digital biomarker for chronotype in bipolar disorder

BackgroundBipolar disorder (BD) is associated with later sleep and daily activity (evening rather than morning chronotype). Objective chronotype identification (e.g., based on actigraphs/smartphones) has potential utility, but to date, chronotype has mostly been assessed by questionnaires. Given the ubiquity of accelerometer-based devices (e.g. actigraphs/smartphones) worn/used during daytime and tendency to recharge rather than wear at night, we assessed chronotype using daytime (rather than sleep) interval midpoints. MethodsSixty-one participants with BD type I (BD-I) or II (BD-II) and 61 healthy controls completed 25–50 days of continuous actigraphy. The Composite Scale of Morningness (CSM) was completed by a subset of this group. Daytime activity midpoint was calculated for each daytime interval, excluding naps. Evening chronotype was defined as having a daytime interval midpoint at or after 16:15:00 (4:15:00 PM). ResultsBD versus controls had delayed daytime midpoint (mean ± standard deviation) (16:49:07 ± 01:26:19 versus 16:12:51 ± 01:02:14, p < 0.01), and greater midpoint variability (73.3 ± 33.9 min versus 58.1 ± 18.3 min, p < 0.01). Stratifying by gender and age, females and adolescents with BD had delayed and more variable daytime midpoints versus controls. Adults with BD had greater midpoint variability than controls. Within-person mean and standard deviations of daytime midpoints were highly correlated with sleep midpoints (r = 0.99, p < 0.01 and r = 0.86, p < 0.01, respectively). Daytime midpoint mean was also significantly correlated with the CSM (r = -0.56, p < 0.01). LimitationsSmall sample size; analyses not fully accounting for daytime napping. ConclusionsWrist actigraphy for determination of daytime midpoints is a potential tool to identify objective chronotype. Exploration of the use of consumer devices (wearables/smartphones) is needed.

A surrogate model based nested optimization framework for inverse problem considering interval uncertainty

The inverse problem is a kind of engineering problem that estimates the input through the given output. In this paper, the given output described as interval uncertainty parameter is concerned, and the interval is formed by the interval midpoint and the interval radius. The two-step framework that estimates the midpoint and the radius separately is used. A novel nested optimization framework is proposed to estimate the input interval radius with more inputs than outputs. The nested framework has two loops: (i) the inner loop quantifies the lower and upper bounds of the output with given interval radiuses of inputs from the outer loop by two optimizations, and the results will be feedback to the outer loop as constraint values of outer loop; (ii) the outer loop maximizes the input interval radiuses to reduce the cost while meeting the constraints transformed from the given interval. The nested framework induces a high number of forward model computations in the loops and may lead to an unacceptable computational burden for most engineering applications. Therefore, the surrogate model is suggested. The Radial Basis Functions (RBF) surrogate model is used to relieve the computational burden. The effectiveness and the accuracy of the framework are verified through a mathematical example, a cantilever tube example and an airfoil example.

On using interval response data in experimental economics

Many empirical applications in the experimental economics literature involve interval response data. Various methods have been considered to treat this type of data. One approach assumes that the data correspond to the interval midpoint and then utilizes ordinary least squares to estimate the model. Another approach is to use maximum likelihood estimation, assuming that the underlying variable of interest is normally distributed. In the case of distributional misspecification, these estimation approaches can yield inconsistent estimators. In this paper, we explore a method that can help reduce the misspecification problem by assuming a distribution that can model a wide variety of distributional characteristics, including possible heteroskedasticity. The method is applied to the problem of estimating the impact of various explanatory factors associated with individual discount rates in a field experiment. Our analysis suggests that the underlying distribution of discount rates exhibits skewness, but not heteroskedasticity, In this example, the findings based on a normal distribution are generally robust across distributions.

Minimizing Bias In Parametric Survival Analyses Of Published Kaplan-Meier Curves

Health economic models often rely on published outcomes such as Kaplan-Meier (KM) curves. Virtual patient-level data (VPLD) can be generated from these curves on which parametric fitting analyses or treatment effects can be evaluated. We evaluated the accuracy of parameters of curves fit to VPLD derived using the Guyot et al. method in a simulation study. We simulated one hundred trials comparing active and reference treatments with Weibull survival times and normal censoring times. The KM curves for both arms were “digitized” under multiple scenarios, varying the number of curve coordinates extracted, and the intervals at which ns at risk are available. The Guyot method was used to generate VPLD from the extracted values. Parameter estimates for Weibull models fit to individual patient-level data (IPD) and VPLD were compared. The shape and scale, but not the treatment effect, were found to be systematically biased. In a digitization scenario with 15 extracted coordinates the median ratio of the VPLD scale to IPD scale was 0.968 (IQR:0.962-0.974) and the median shape ratio was 1.176 (IQR:1.166-1.206). Increasing the number of coordinates extracted reduced, but did not eliminate the bias. The interval at which the ns at risk were reported had no apparent effect on the bias. Moving virtual events to interval midpoints from interval endpoints changed the sign of and markedly reduced the bias, in the example digitization the median scale ratio became 1.002 (IQR:1.001-1.004) and the median shape ratio became 0.979 (IQR:0.965-0.996). To eliminate bias, it was necessary to both increase the number of extracted coordinates and place events at interval midpoints. Placing events at the end of time intervals in VPLD may bias survival projections. The bias can be minimized by extracting the greatest number of KM coordinates feasible and by placing events at interval midpoints.

Subjective versus objective evening chronotypes in bipolar disorder

BackgroundDisturbed sleep timing is common in bipolar disorder (BD). However, most research is based upon self-reports. We examined relationships between subjective versus objective assessments of sleep timing in BD patients versus controls. MethodsWe studied 61 individuals with bipolar I or II disorder and 61 healthy controls. Structured clinical interviews assessed psychiatric diagnoses, and clinician-administered scales assessed current mood symptom severity. For subjective chronotype, we used the Composite Scale of Morningness (CSM) questionnaire, using original and modified (1, ¾, ⅔, and ½ SD below mean CSM score) thresholds to define evening chronotype. Objective chronotype was calculated as the percentage of nights (50%, 66.7%, 75%, or 90% of all nights) with sleep interval midpoints at or before (non-evening chronotype) vs. after (evening chronotype) 04:15:00 (4:15:00a.m.), based on 25–50 days of continuous actigraph data. ResultsBD participants and controls differed significantly with respect to CSM mean scores and CSM evening chronotypes using modified, but not original, thresholds. Groups also differed significantly with respect to chronotype based on sleep interval midpoint means, and based on the threshold of 75% of sleep intervals with midpoints after 04:15:00. Subjective and objective chronotypes correlated significantly with one another. Twenty-one consecutive intervals were needed to yield an evening chronotype classification match of ≥ 95% with that made using the 75% of sleep intervals threshold. LimitationsLimited sample size/generalizability. ConclusionsSubjective and objective chronotype measurements were correlated with one another in participants with BD. Using population-specific thresholds, participants with BD had a later chronotype than controls.