Cubic Model Research Articles

Experimental and theoretical bifurcation study of a nonlinear standing-wave thermoacoustic system

In this work, both theoretical and experimental bifurcation studies of nonlinear standing-wave thermoacoustic systems are performed. To characterize the unsteady heat release, two different models are proposed to approximate experimental measurements of the response of a premixed flame to acoustic waves. Model A is formulated with 3rd order polynomial equation, while model B is 5th order one. The expansion method of Galerkin series is applied to decouple the unsteady acoustic field in the spatial and time domains. Multiple scales method is proposed to extract the essential dynamic behaviors from the governing ordinary differential equations. The process of the thermoacoustic system's transition to instability is evaluated by continuation methods. Model A is shown to be associated with a supercritical Hopf bifurcation. However, subcritical Hopf bifurcation occurs in the higher-order modelled nonlinear thermoacoustic system, i.e. model B. Furthermore, hysteresis and bistable zones are observed. In addition, the effects of 1) the heating power K, 2) the axial location of the heat source xf/L and 3) the overall acoustic damping/loss ξ on supercritical and subcritical bifurcations are studied one at a time. To validate our theoretical findings on supercritical and subcritical bifurcation, experimental investigation on a standing-wave Rijke tube with a premixed flame confined is conducted. It is observed that varying the flame axial location xf/L can destabilize the thermoacoustic system via either subcritical or supercritical bifurcation on two different operation conditions. In addition, the measured bifurcation behaviors show a good qualitative agreement with the theoretical findings.

Validation of a novel nonlinear black box Wiener System model for arterial pulse transmission

Numerous linear dynamic models exist for describing the arterial pulse transmission phenomenon. We introduce a novel Wiener system based model in which a linear filter representing large arteries is coupled with a hysteresis-free nonlinear function representing complex wave transmission of branching arteries and the periphery. Experimental datasets (n = 7) are used to first estimate the Wiener model with linear, quadratic and cubic function for the aorta to radial artery pulse transmission and aorta to femoral artery pulse transmission. To model the nonlinear memoryless monotonic function in the Wiener System model, a correlation study is performed for linear finite impulse response (FIR) filter simulated peripheral pressure vs. measured peripheral pressure waveform. Each of this correlation curves were fitted to linear, quadratic and cubic polynomial equation. Wiener model is then simulated for aortic-to-radial artery as well as aortic-to-femoral artery to reconstruct radial and femoral pressure waveform. It was found that Wiener model with 3rd order polynomial function yielded better modeling accuracy (with average RMSE = 2.187 mmHg for radial and 4.281 mmHg for femoral pressure) than that from 2nd order polynomial function (with average RMSE = 2.242 mmHg for radial and 4.355 mmHg for femoral pressure) which in turn was better than mere linear FIR filter (with average RMSE = 2.604 mmHg for radial and 4.810 mmHg for femoral pressure).

Temperature dependent development of Phenacoccus solenopsis under laboratory conditions

Cotton mealybug, Phenacoccus solenopsis Tinsley (Hemiptera: Pseudococcidae) is an important cotton pest in Punjab, India. Development of the immature stages (four instars in female and five in male) of P. solenopsis was observed at nine constant temperatures (15, 18, 20, 25, 30, 34, 35, 38, 40°C). Using the linear model, the lower temperature threshold (tmin) for development was estimated to be 4.93 and 2.95°C and the thermal constant (K) was 333.33 and 454.54 degree days for female and male, respectively. In addition, three nonlinear models (Lactin, Bieri-1 and 3rd order polynomial) were tested to describe the relationship between temperature and development rate and to estimate the upper developmental threshold (tmax) and the optimum temperature for development (topt). Our results proved that the Bieri-1 and Lactin models and provided the best fit (r2 = 93,4 – 99,9%) and estimated accurately all the three critical temperatures, ranged tmin = 5.06 – 5.25°C, topt = 33.55 – 33.60°C, tmax = 39.99 – 40.00°C, for the total development of females and tmin = 2.82 – 3.16°C, topt = 34.01 – 34.04°C, tmax =40.00 – 40.10°C, for the total development of males.

Multi-segmental thoracic spine kinematics measured dynamically in the young and elderly during flexion

In contrast to the cervical and lumbar region, the normal kinematics of the thoracic spine have not been thoroughly investigated. The aim of this study was to characterize normal multi-segmental continuous motion of the whole thoracolumbar spine, during a flexion maneuver, in young and elderly subjects. Forty-two healthy volunteers were analyzed: 21 young (age=27.00±3.96) and 21 elderly (age=70.1±3.85). Spinal motion was recorded with a motion-capture system and analyzed using a 3rd order polynomial function to approximate spinal curvature throughout the motion sequence. The average motion profiles of the two age groups were characterized. Flexion timing of the thoracic region of the spine, as compared to the lumbar spine and hips, was found to be different in the two age groups (p=0.011): a delayed/sequential motion type was observed in most of the young, whereas mostly a simultaneous motion pattern was observed in the elderly subjects. A similar trend was observed in flexion of the lower thoracic segments (p=0.017). Differences between age groups were also found for regional and segmental displacements and velocities. The reported characterization of the thoracic spine kinematics may in the future support identification of abnormal movement or be used to improve biomechanical models of the spine.

Prediction of Critical Power and W′ in Hypoxia: Application to Work-Balance Modelling

Purpose: Develop a prediction equation for critical power (CP) and work above CP (W′) in hypoxia for use in the work-balance () model.Methods: Nine trained male cyclists completed cycling time trials (TT; 12, 7, and 3 min) to determine CP and W′ at five altitudes (250, 1,250, 2,250, 3,250, and 4,250 m). Least squares regression was used to predict CP and W′ at altitude. A high-intensity intermittent test (HIIT) was performed at 250 and 2,250 m. Actual and predicted CP and W′ were used to compute W′ during HIIT using differential () and integral () forms of the model.Results: CP decreased at altitude (P < 0.001) as described by 3rd order polynomial function (R2 = 0.99). W′ decreased at 4,250 m only (P < 0.001). A double-linear function characterized the effect of altitude on W′ (R2 = 0.99). There was no significant effect of parameter input (actual vs. predicted CP and W′) on modelled at 2,250 m (P = 0.24). returned higher values than throughout HIIT (P < 0.001). During HIIT, was not different to 0 kJ at completion, at 250 m (0.7 ± 2.0 kJ; P = 0.33) and 2,250 m (−1.3 ± 3.5 kJ; P = 0.30). However, was lower than 0 kJ at 250 m (−0.9 ± 1.3 kJ; P = 0.058) and 2,250 m (−2.8 ± 2.8 kJ; P = 0.02).Conclusion: The altitude prediction equations for CP and W′ developed in this study are suitable for use with the model in acute hypoxia. This enables the application of modelling to training prescription and competition analysis at altitude.

Anisotropic and temperature-dependent thermal conductivity of PbI2

The temperature-dependent components of the anisotropic thermal diffusivity of lead iodide (PbI2) have been measured by Laser Flash Analysis (LFA). The temperature range used was −100°C to +350°C. The temperature-dependent specific heat capacity cp was determined independently by Differential Scanning Calorimetry (DSC) to calculate the thermal conductivities for PbI2 from the thermal diffusivity data. At 27°C, the thermal conductivity in the c-axis-direction, k33, is 0.315Wm−1K−1, whereas the component perpendicular to the c-axis, k11, is 0.681Wm−1K−1. The anisotropy ratio k33/k11 changes from 1:2 at −100°C to 1:2.4 at +350°C. The temperature dependencies of both k33 and k11 in this range can be very well fitted with 3rd order polynomials.

Performance verification of laboratory-developed clinical chemistry system-Analytical measurement range and clinical reportable range

Objective To estimate the methodology for evaluating the analytical measurement range (AMR) and the clinically reportable range (CRR) in lab-developed system in clinical chemistry. Methods Method evaluation.Take serum CK for instance, a series of samples were prepared from both a specimen with a high concentration of the analyte of interest and a specimen with a low concentration for the following assays.Average slope method, linear dilution recovery method and the method recommended by Clinical and Laboratory Standards Institute (CLSI) EP6-A were used to established AMR in the lab-developed clinical chemistry system. Based on the maximum valid dilution of the specimen and the results of AMR, CRR were determined. One-half of the total error allowance (TEa) of Chinese health standard was set up as allowance error (7.5%). Results X-Y scatter plot was made by assigning sample numbers to the horizontal axis and actual measured values to the vertical axis, which determined the upper limit of AMR was approximate 1 651 U/L. The results analyzed by average slope method indicated that the linear correlation between expected values and actual measured values was determined, the correlation (r), the intercept (a) and the slope (b) met the linear standard, and AMR was 5-1 699 U/L. The results analyzed by EP6-A indicated that the best fitting curve was obtained by using cubic polynomial method, and the linearity deviation of the minimum concentration was -77.1%, which exceeded one-half of TEa. Followed by the deletion of the maximum concentration, the resumed experiment was done. The results showed that the nonlinear coefficient c of quadratic polynomial and the nonlinear coefficient c and d of cubic polynomial have no significant difference to 0, and AMR was 7.5-1 458.0 U/L. By linear dilution recovery method, the linear correlation between expected values and actual measured values was determined, the correlation (r), the intercept (a) and the slope (b) met the linear standard, the recovery rates was between 100.0% and 104.8%, and AMR is 5-1 699 U/L. The CRR was determined to be 5-33 880 U/L, which met the standard of TEa. Conclusions Average slope method, linear dilution recovery method and EP6-A method were all used to established AMR in lab-developed clinical chemistry system. Without complicated statistical analysis, linear dilution recovery method was suitable for clinical use. The linearity deviation of the minimum concentration analyzed by EP6-A did not meet the standard of the quality objective system, suggesting defects in the statistical analysis of the results.CRR was feasibly determined by using linear dilution recovery method align with AMR.(Chin J Lab Med, 2016, 39: 946-952) Key words: Creatine kinase; Clinical chemistry tests; Evaluation studies

Implementation of a sigmoid depth function to describe change of soil pH with depth

Soil pH controls the availability of the majority of plant nutrients, if not all, and determines the growth environment for plant roots. Profile depth functions have been used to represent the vertical distribution of soil attributes and to predict them at continuous depths. This paper proposes a new model to predict pH for a whole soil profile. Soil properties including pH are often similar within the plow layer from mixing during tillage and other agricultural operations. Similarly, soil pH below the root zone tends to be uniform due to low disturbance, leaving a transition zone from the bottom of the tillage layer to the bottom of the root zone due to depth-dependent root density and related soil processes. Keeping this physical description of agricultural field soil profile in mind, a closed form equation (model) was developed similar to a sigmoid curve. The model has 4 parameters including 1) soil pH at the top of a soil profile, 2) soil pH at the bottom of a soil profile, 3) hillslope parameter representing steepness of the curve that is determined by the length of the root zone, and 4) inflection point representing almost the midpoint of the transition zone or root zone. A total of 32 soil cores down to about 1.1m depths were collected from an agricultural field of Macdonald farm, McGill University. The sub-samples were taken at every 10cm and analyzed for soil pH in soil: water suspension in the laboratory. The measured pH was used to test the fitting performance of the sigmoid model. Additionally, a global dataset with 432 profiles with various soil classes, drainage types, land use, and altitude was also used to test the generality of the new model. The performance of this model was compared with the results of the commonly used 3rd order polynomial regression function and the equal-area quadratic spline function. Good performance of the sigmoid model with explicit physical explanation showed promise in predicting soil pH at depths. The spline function had the highest accuracy but lacked a general trend in its shape and parameters. The polynomial function had good accuracy and displayed a non-monotonic trend, which can also be used as a substitute for some profiles with complex variability.

Differentiation of foodborne bacteria using NIR hyperspectral imaging and multivariate data analysis.

The potential for near-infrared (NIR) hyperspectral imaging and multivariate data analysis to be used as a rapid non-destructive tool for detection and differentiation of bacteria was investigated. NIR hyperspectral images were collected of Bacillus cereus, Escherichia coli, Salmonella enteritidis, Staphylococcus aureus and Staphylococcus epidermidis grown on agar for 20h at 37°C. Principal component analysis (PCA) was applied to mean-centred data. Standard normal variate (SNV) correction and the Savitzky-Golay technique was applied (2nd derivative, 3rd-order polynomial; 25 point smoothing) to wavelengths in the range of 1103 to 2471nm. Chemical differences between colonies which appeared similar in colour on growth media (B. cereus, E. coli and S. enteritidis.) were evident in the PCA score plots. It was possible to distinguish B. cereus from E. coli and S. enteritidis along PC1 (59% sum of squares (SS)) and between E. coli and S. enteritidis in the direction of PC2 (6.85 % SS). S. epidermidis was separated from B. cereus and S. aureus along PC1 (37.5% SS) and was attributed to variation in amino acid and carbohydrate content. Two clusters were evident in the PC1 vs. PC2 PCA score plot for the images of S. aureus and S. epidermidis, thus permitting distinction between species. Differentiation between genera (similarly coloured on growth media), Gram-positive and Gram-negative bacteria and pathogenic and non-pathogenic species was possible using NIR hyperspectral imaging. Partial least squares discriminant analysis (PLS-DA) models were used to confirm the PCA data. The best predictions were made for B. cereus and Staphylococcus species, where results ranged from 82.0 to 99.96% correctly predicted pixels.

Optimising prediction model of centrifugal pump as turbine with viscosity effects

Performance conversion of a centrifugal pump as turbine from the known performance curves in pump mode is vital important in pump selection, power generation and investment assessment, especially under low Reynolds number operation conditions. Effects of Reynolds number on such a performance conversion have not been taken into account so far. In the paper, flow rate, head and output power and hydraulic efficiency conversion factors at zero efficiency/power, 0.8 part-load, best efficiency, 1.2 over-load and maximum flow rate points are defined and extracted from the performance curves of a centrifugal pump as turbine at five viscosities obtained by using CFD simulations. The conversion factors are correlated to impeller Reynolds number and a performance conversion model is proposed by employing 3rd and 4th order polynomials for the output power and head curves. New correlations of flow rate, head and efficiency conversion factors are also attempted in terms of specific speed and efficiency as well as impeller Reynolds number based on the data found in literature. The conversion model is a framework and can be useful for design of pump as turbine and its performance prediction, especially under variable liquid viscosity conditions.

A 3rd-order polynomial temperature profile model for the heating and evaporation of moving droplets

Droplet heating and evaporation is of fundamental importance in various engineering applications. Based on the assumption that droplets’ internal temperature follows a third-order polynomial distribution, a new liquid phase model is proposed, taking into account both temperature gradient and internal circulation inside the droplet in terms of Hill’s spherical vortex. The new liquid model and other commonly used liquid models are compared with the experimental data outlined in the literature. The internal temperature predicted by the new model matches the experimental data of an n-Decane droplet heating best, whereby the enhancement of heat transport by internal circulation is correctly reflected. In comparison, other models always predict the monotonic variation of internal temperature during the initial heating period, which deviates widely from the experimental data. The new model displays the best performance with regard to predicting droplet evaporation in the later vaporizing period, whereas the parabolic temperature profile model and conduction limit model significantly underestimate and overestimate the droplet evaporation rate, respectively. The CPU requirement for the new model is far less than that for the conduction limit model and the effective thermal conductivity model with an order of magnitude, which shows its potential for implementation into CFD codes.

Application of high resolution OCT to evaluate irregularity of Bowman's layer in asymmetric keratoconus.

Irregularity of the Bowman's layer (BL) in keratoconus (KC, sample size (n) = 28) and forme fruste keratoconus (FFKC, n=18) eyes was evaluated. Subjects underwent high resolution OCT imaging (Bioptigen Inc., USA) and corneal tomography (Pentacam v1.20r41, OCULUS Optikgeräte GmbH, Germany). Anterior edge of the BL was segmented. A Bowman's roughness index (BRI) was defined as the sum of the enclosed areas between segmented edge and a smooth 3rd order polynomial fit to the edge. BRI was compared with corneal aberrations, Keratoconus percentage index (KISA), Cone location magnitude index (CLMI) and Belin-Ambrosio enhanced ectasia display overall deviation index (BAD-D). Area under the curve (AUC) was determined with logistic regression (LR). Mean BRI (×10-3 ) was 2.12 mm2 , 1.81 mm2 and 1.7 mm2 in normal (n=26), FFKC and KC eyes, respectively (p<0.001). BAD-D (0.79) and BRI (0.74) had the best AUC for FFKC. By combining BAD-D and BRI, the AUC improved to 0.85 (p=0.01). For KC eyes, KISA (0.94), CLMI (0.88), BAD-D (0.96) and aberrations had comparable AUC (p>0.05). However, LR with BRI and other indices didn't improve the AUC in KC eyes (p>0.05). BRI was significantly reduced in FFKC and KC eyes. It improved the detection of FFKC but not KC eyes.

Effect of process conditions on Fischer–Tropsch synthesis product selectivity over an industrial iron-based catalyst in slurry reactor

ABSTRACTThe authors present the application of the statistical model in CO hydrogenation to CH4, C2-C4 and C5+ over industrial iron-based catalyst (100 Fe/5 Cu/4.2 K/25 SiO2) in a 1-L stirred tank slurry reactor. The effect of different reaction conditions, including temperatures (T = 493, 513 and 533 K), pressures (P = 0.8, 1.5, 2.25, and 2.5 MPa), synthesis gas feed molar ratios (H2/CO = 0.67 and 2), and gas space velocity (GSV) from 0.52 to 23.5 Ndm3/g-Fe/h on selectivity investigated via a statistical models. The proposed selectivity model is very useful in the oil, gas, and petrochemical industries and can be used for interpretation of experimental data, comparison of performance of different reactor conditions, and reactor modeling and simulation studies. Furthermore, interaction between operating parameters such as pressure, temperature, H2/CO, and GSV was investigated in selectivity models. A CUBIC polynomial was successfully fitted to the experimental data. It was concluded that C5+ selectivity shifts to higher with increasing total pressure (H2/CO) ratio and decreasing temperature. Decreased H2/CO ratio and temperature and increasing in the reactor pressure cause CH4 formation decrease. Temperature and pressure fluctuations vary product distribution. As it is observed, the insignificant term in C2-C4 selectivity is pressure. With the models obtained from regression we can reach to the optimum condition for favorite products such as C2-C4 or C5+. So that optimization must be done to illustrate the optimum conditions. It was obtained that the maximum amount of C5+ and C2-C4 and minimum amount of methane achieved in T = 528.97 K, P = 1.23 bar, H2/CO = 2, and GSV = 23.49 Ndm3/g-Fe/h.

MODELLING THE TEMPERATURE-MYCELIAL GROWTH RATE RELATIONSHIPS IN FUNGI RHIZOCTONIA spp.

Temperature is one of the most important factors affecting the fungal growth and development and their relationships have been investigated in physiological and epidemiological studies. Cardinal temperatures of fungi were obtained from these studies and they were mainly performed via visual estimation of polynomial modeling, which resulted in non-biologically meaningful parameters. In this study, eight nonlinear regression models were used for modeling temperature-mycelial growth rate relationships of three anastomosis groups of Rhizoctonia spp. (AG 1-IA, AG 4 and WAG-Z). Comparison and selection of the best-fitting model were conducted based on SE, adjusted R2, RMSE, a, and b, and they were then ranked by AIC statistic. The results indicated that the segmented model was the best fit for all three AGs. Based on AICc and i, the segmented model was the best fit model for describing growth rate of AG 4 and WAG-Z at different temperatures. In case of AG 1-IA, the cubic model could produce the least amount of AICc and the segmented model ranked second. Besides, i of dent-like model was <10 in all three cases and, therefore there was not a significant difference in fitness of these models. Estimated Tb and (Tc) of AG 1-IA, AG 4 and WAG-Z by the segmented model were 7.94, (38.69)°C, 7.66, (39.59)°C and 8.11, (41)°C, respectively. Optimum temperatures estimated by the segmented model for AG 1-IA, AG 4 and WAG-Z were 28.58°C, 29.99°C and 33.72°C, respectively.

State of health monitoring in machining: Extended Kalman filter for tool wear assessment in turning of IN718 hard-to-machine alloy

An extended Kalman filter (EKF) is employed in this work for tracking tool flank wear area in wet-turning of Inconel 718 (IN718) nickel-based alloy in variable feed condition. The tool wear area evolution is modeled with a 3rd order polynomial empirical function and an analytical solution for discrete state space system is derived. The state uncertainty was found to decrease up to a critical range of 200–250μm of average flank wear length, and then increase abruptly with an increase in tool wear. Therefore, the tool wear uncertainty was modeled with failure probability density, i.e. the bathtub function, while a constant uncertainty was considered for the measurement signal (spindle power). To demonstrate the significance of using this method, the root mean square error (RMSE) and the mean absolute error (MAE) were calculated and compared with deterministic method in estimation of the tool wear area. It was shown that the proposed estimation based on stochastic filter EKF increased the accuracy of estimation by maximum of 60%. Results for estimation of the rate of tool wear area indicate additional possible effects or transitions of effects at higher wear conditions.

A Doubly Curved Axisymmetric Finite Element for Subsea Sandwich Domes

THE PAPER FOCUSES ON THE ANALYSIS OF SANDWICH DOMES USING A NEWLY DEVELOPED DOUBLY CURVED AXISYMMETRIC SANDWICH FINITE ELEMENT. THE SIMPLE EQUIVALENT SINGLE LAYER FINITE ELEMENT EMPLOYS A CUBIC POLYNOMIAL APPROXIMATION FOR TRANSVERSE DISPLACEMENT AND MERIDIONAL DISPLACEMENT. THE PRESENT ELEMENT ACCOUNTS FOR THE TRANSVERSE SHEAR STRAINS OF THE FACING AND CORE USING QUADRATIC POLYNOMIAL. THE RELATION BETWEEN INPLANE STRESSES AND STRAINS FOR AXISYMMETRIC DEFORMATION HAS BEEN REPRESENTED BY A STATE OF GENERALIZED PLANE STRESS. THE STIFFNESS MATRIX HAS BEEN DERIVED USING THE VARIATIONAL PRINCIPLE. THE NUMERICAL EXAMPLES HAVE BEEN PRESENTED TO ILLUSTRATE THE ELEMENT CAPABILITIES AND ACCURACY OF THE RESULTS ACHIEVED USING THE NEWLY DEVELOPED SANDWICH SHELL ELEMENT.

Chronology of fluvial terrace sequences for large Atlantic rivers in the Iberian Peninsula (Upper Tagus and Duero drainage basins, Central Spain)

This work analyses the chronology of fluvial terrace sequences of the two most important fluvial basins from central Spain draining to the Atlantic Ocean (Upper Tagus and Duero drainage basins). Both basins evolved under similar Mediterranean climatic conditions throughout the Pleistocene and present comparable number of fluvial terraces (16–17) after excluding the higher terrace levels of the Tagus (T1–T5) entrenched in the Raña surface. These higher “rañizo terraces” was formed in response to fan-head trenching in this high alluvial piedmont (+220 m) and therefore not properly controlled by Quaternary fluvial downcutting. The study accomplishes the implementation of multiple regression analyses for terrace height-age relationships. To transform relative terrace heights above the present river thalwegs (i.e. +100 m) in numerical ages a “height-age transference function” has been developed on the basis of preliminary statistical geochronological approaches proposed for Central Spain. The resultant height-age transference function gather 73 published geochronological data for terrace sequences, featuring a 3rd Order Polynomial Function (R2 0.90). This function describes the overall trend of valley downcutting for the last c. 2.3 Ma in Central Spain and is used to assign numerical ages to terrace levels at different relative elevation.

A Greedy reassignment algorithm for the PBS minimum monitor unit constraint

Proton pencil beam scanning (PBS) treatment plans are made of numerous unique spots of different weights. These weights are optimized by the treatment planning systems, and sometimes fall below the deliverable threshold set by the treatment delivery system. The purpose of this work is to investigate a Greedy reassignment algorithm to mitigate the effects of these low weight pencil beams. The algorithm is applied during post-processing to the optimized plan to generate deliverable plans for the treatment delivery system. The Greedy reassignment method developed in this work deletes the smallest weight spot in the entire field and reassigns its weight to its nearest neighbor(s) and repeats until all spots are above the minimum monitor unit (MU) constraint. Its performance was evaluated using plans collected from 190 patients (496 fields) treated at our facility. The Greedy reassignment method was compared against two other post-processing methods. The evaluation criteria was the γ-index pass rate that compares the pre-processed and post-processed dose distributions. A planning metric was developed to predict the impact of post-processing on treatment plans for various treatment planning, machine, and dose tolerance parameters. For fields with a pass rate of 90 ± 1% the planning metric has a standard deviation equal to 18% of the centroid value showing that the planning metric and γ-index pass rate are correlated for the Greedy reassignment algorithm. Using a 3rd order polynomial fit to the data, the Greedy reassignment method has 1.8 times better planning metric at 90% pass rate compared to other post-processing methods. As the planning metric and pass rate are correlated, the planning metric could provide an aid for implementing parameters during treatment planning, or even during facility design, in order to yield acceptable pass rates. More facilities are starting to implement PBS and some have spot sizes (one standard deviation) smaller than 5 mm, hence would require small spot spacing. While this is not the only parameter that affects the optimized plan, the perturbation due to the minimum MU constraint increases with decreasing spot spacing. This work could help to design the minimum MU threshold with the goal to keep the γ-index pass rate above an acceptable value.

TH‐CD‐209‐01: A Greedy Reassignment Algorithm for the PBS Minimum Monitor Unit Constraint

Purpose:To investigate a Greedy Reassignment algorithm in order to mitigate the effects of low weight spots in proton pencil beam scanning (PBS) treatment plans.Methods:To convert a plan from the treatment planning system's (TPS) to a deliverable plan, post processing methods can be used to adjust the spot maps to meets the minimum MU constraint. Existing methods include: deleting low weight spots (Cut method), or rounding spots with weight above/below half the limit up/down to the limit/zero (Round method). An alternative method called Greedy Reassignment was developed in this work in which the lowest weight spot in the field was removed and its weight reassigned equally among its nearest neighbors. The process was repeated with the next lowest weight spot until all spots in the field were above the MU constraint. The algorithm performance was evaluated using plans collected from 190 patients (496 fields) treated at our facility. The evaluation criteria were the γ‐index pass rate comparing the pre‐processed and post‐processed dose distributions. A planning metric was further developed to predict the impact of post‐processing on treatment plans for various treatment planning, machine, and dose tolerance parameters.Results:For fields with a gamma pass rate of 90±1%, the metric has a standard deviation equal to 18% of the centroid value. This showed that the metric and γ‐index pass rate are correlated for the Greedy Reassignment algorithm. Using a 3rd order polynomial fit to the data, the Greedy Reassignment method had 1.8 times better metric at 90% pass rate compared to other post‐processing methods.Conclusion:We showed that the Greedy Reassignment method yields deliverable plans that are closest to the optimized‐without‐MU‐constraint plan from the TPS. The metric developed in this work could help design the minimum MU threshold with the goal of keeping the γ‐index pass rate above an acceptable value.

Prediction of Bankruptcy with SVM Classifiers Among Retail Business Companies in EU

Article focuses on the prediction of bankruptcy of the 850 medium-sized retail business companies in EU from which 48 companies gone bankrupt in 2014 with respect to lag of the used features. From various types of classification models we chose Support vector machines method with linear, polynomial and radial kernels to acquire best results. Pre-processing is enhanced with filter based feature selection like Gain ratio, Chi-square and Relief algorithm to acquire attributes with the best information value. On this basis we deal with random samples of financial data to measure prediction accuracy with the confusion matrices and area under curve values for different kernel types and selected features. From the results it is obvious that with the rising distance to the bankruptcy there drops precision of bankruptcy prediction. The last year (2013) with avaible financial data offers best total prediction accuracy, thus we also infer both the Error I and II types for better recognizance. The 3rd order polynomial kernel offers better accuracy for bankruptcy prediction than linear and radial versions. But in terms of the total accuracy we recommend to use radial kernel without feature selection.