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The most widely used formula for estimating glomerular filtration rate (eGFR) in children is the Schwartz formula. It was revised in 2009 using iohexol clearances with measured GFR (mGFR) ranging between 15 and 75ml/min × 1.73m2. Here we assessed the accuracy of the Schwartz formula using the inulin clearance (iGFR) method to evaluate its accuracy for children with less renal impairment comparing 551 iGFRs of 392 children with their Schwartz eGFRs. Serum creatinine was measured using the compensated Jaffe method. In order to find the best relationship between iGFR and eGFR, a linear quadratic regression model was fitted and a more accurate formula was derived. This quadratic formula was: 0.68 × (Height (cm)/serum creatinine (mg/dl))-0.0008 × (height (cm)/serum creatinine (mg/dl))2+0.48 × age (years)-(21.53 in males or 25.68 in females). This formula was validated using a split-half cross-validation technique and also externally validated with a new cohort of 127 children. Results show that the Schwartz formula is accurate until a height (Ht)/serum creatinine value of 251, corresponding to an iGFR of 103ml/min × 1.73m2, but significantly unreliable for higher values. For an accuracy of 20 percent, the quadratic formula was significantly better than the Schwartz formula for all patients and for patients with a Ht/serum creatinine of 251 or greater. Thus, the new quadratic formula could replace the revised Schwartz formula, which is accurate for children with moderate renal failure but not for those with less renal impairment or hyperfiltration.

This paper explains the steps used to find the characteristic polynomial of the antiadjacency matrix of a cyclic dumbbell graph. The antiadjacency matrix of a graph is a matrix whose entries represent whether there is an edge that connects two vertices or not. The general form of the characteristic polynomial includes its eigenvalues. The antiadjacency matrix is obtained by using some theorems, the number of solutions of integer equations, quadratic formula, and polynomials factorization. Finally, results showed that the coefficients of the characteristic polynomial and its eigenvalues were dependent on the number of vertices of the cyclic dumbbell graph.

This paper discusses the application of a constraint-based model predictive control (MPC) to mobile manipulation tracking problems. The problem has been formulated so as to guarantee offset-free tracking of piecewise constant references, with convergence and recursive feasibility guarantees. Since MPC inputs are recomputed at every control iteration, it is possible to deal with dynamic and unknown scenarios. A number of motion constraints can also be easily included: Acceleration, velocity and position constraints have been enforced, together with collision avoidance constraints for the mobile base and the arm and field-of-view constraints. Such constraints have been extended over the prediction horizon maintaining a linear-quadratic formulation of the problem. Navigation performance has been improved by devising an online algorithm that includes an additional goal to the problem, derived from the classical vortex field approach. Experimental validation shows the applicability of the proposed approach.

Split quaternions are noncommutative and contain nontrivial zero divisors. Generally speaking, it is difficult to solve equations in such an algebra. In this paper, by using the roots of any split quaternions and two real nonlinear systems, we derive explicit formulas for computing the roots of x2+bx+c=0 in split quaternion algebra.

In order to propose a deeper analysis of the general quartic equation with real coefficients, the analytical solutions for all cubic and quartic equations were reviewed here; then, it was found that there can only be one form of the resolvent cubic that satisfies the following two conditions at the same time: (1) Its discriminant is identical to the discriminant of the general quartic equation. (2) It has at least one positive real root whenever the general quartic equation is non-biquadratic. This unique special form of the resolvent cubic is defined here as the “Standard Form of the Resolvent Cubic”, which becomes relevant since it allows us to reveal the relationship between the nature of the roots of the general quartic equation and the nature of the roots of all the forms of the resolvent cubic. Finally, this new analysis is the basis for designing and programming efficient algorithms that analytically solve all algebraic equations of the fourth and lower degree with real coefficients, always avoiding the application of complex arithmetic operations, even when these equations have non-real complex roots.

•Single bullet impacts in thin metal are common at crime scenes.•Extrapolation of trajectory and shooter placement from these impacts is error prone.•Using the Ellipser App in CloudCompare, impact angles were measured using the best-fit ellipse method.•Preliminary results suggest single bullet impacts have characteristic error patterns from low to high impact angles.•Ammunition type has a significant effect on the error pattern. Using the best-fit ellipse method, single bullet impacts in thin sheet metal were assessed to investigate the accuracy of impact angle estimation. When a bullet passes through a metal panel, the yielding nature of metal causes changes to the metal surface and the resultant hole. This deformation of the metal complicates the assessment of single impacts using the ellipse method. Determining the correct impact angle may not be obvious and results in considerable errors between the known and calculated angle. To determine if the calculated angle varies in any particular way to the known angle, impacts were created on metal panels using six different types of 9 mm ammunition and seven angles from 90° to 14°. Impact angles, determined using the ellipse method, were compared with known firing angles and the error pattern assessed. The results show an error pattern with a significant quadratic relationship for three ammunition types, with the error pattern for the remaining three ammunitions not explained by a quadratic formula and requiring further study. Results suggest that single bullet impacts for a given type of ammunition with a quadratic error pattern, can be assessed with accuracy due to a more consistent behavior. This characteristic pattern of error requires further study but is a promising step for determining an accurate impact angle and bullet path from a single impact point in a metal surface.

The Extreme ultraviolet Imaging Spectrometer (EIS) on board the Hinode spacecraft has been operating since 2006, returning high-resolution data in the 170 – 212 and 246 – 292 Å wavelength regions. EIS has four slit options, with the narrow 1′′ and 2′′ slits used for spectroscopy and the wide 40′′ and 266′′ slits used for monochromatic imaging. In this article several properties of the 40′′ slit (or slot) are measured using the Fe XII 195.12 Å line, which is formed at 1.5 MK. The projected width of the slot on the detector shows a small variation along the slit with an average value of 40.949′′. The slot image is tilted on the detector and a quadratic formula is provided to describe the tilt. The tilt corresponds to four pixels on the detector and the slot centroid is offset mostly to the right (longer wavelengths) of the 1′′ slit by up to four pixels. Measurement of the intensity decrease at the edge of the slot leads to an estimate of the spatial resolution of the images in the x-direction. The resolution varies quadratically along the slot, with a minimum value of 2.9′′ close to the detector center. Intensities measured from the slot images are found to be on average 14% higher than those measured from the 1′′ slit at the same spatial location. Background subtraction is necessary to derive accurate intensities in quiet-Sun and coronal-hole regions. Prescriptions for deriving accurate slot intensities for different types of slot datasets are presented.

BackgroundNeonatal diseases differ depending on gestational age and weight. In the setting of an emergency in the neonatal intensive care unit (NICU), relevant clinical information is often not available when the first neonatal radiograph is obtained. When reading an initial chest-abdomen radiograph, the paediatric radiologist needs gestational age data for best radiologic practice. A transverse diameter of the chest has been previously described to estimate gestational age (GA).ObjectivesTo determine the strength of the correlation between GA/weight and clavicular-pubis length (CPL) on admission radiographs; to obtain a quadratic formula based on the correlation of CPL with GA and to demonstrate if a more simplified formula used by our group works as efficiently as the formula provided by the regression analysis.Materials and methodsA retrospective study was approved by the institutional review board and informed consent was waived. The length from the medial aspect of the clavicle to the pubic bone was measured on the initial portable chest-abdomen radiographs of 260 patients admitted to the NICU in 2016. Regression analysis was performed to investigate the association between CPL and GA/birth weight.ResultsOne hundred eleven females and 149 males with GA between 23 and 42 weeks were evaluated. CPL was statistically associated with both GA (P<0,01) and birth weight. The estimation can be expressed with an equation of the model: GA (weeks) = (CPL in cm – 1.98)/0.42. A simplified formula: GA (weeks) = (CPL in cm) ×2+2, strongly correlates with the equation model.ConclusionIn patients in whom it is not known, GA can be estimated by measuring the length between medial clavicle and symphysis pubis using the formulae we propose.

Autosomal dominant polycystic kidney disease (ADPKD) is an inherited disorder characterized by renal tubular cystic dilatations. The cysts can develop anywhere along the nephron, and over time the cystic dilatation leads to kidney enlargement. On the other hand, the cysts begin to reduce the number of functional nephrons as a consequence of cystic expansion that further contributes to the decline in renal function over the years. The pressure exerted by the dilated cysts leads to compensatory mechanisms that further contribute to the decline in renal function. These structural changes are responsible of glomerular hyperfiltration states, albuminuria, proteinuria, and hematuria. However, the presentation of ADPKD varies in children, from a completely asymptomatic child with incidental ultrasound detection of cysts to a rapidly progressive disease. There have been reports of early onset ADPKD in children younger than 2 years that showed a more rapid decline in renal function. ADPKD is caused by a mutation in PKD1 and PKD2 genes. Today, the PKD1 gene mutation seems to account for up to 85% of the cases worldwide, and it is associated with worse renal outcomes. Individuals with PKD2 gene mutation seem to present a milder form of the disease, with a more delayed onset of end-stage kidney disease. The cardinal sign of ADPKD is the presence of renal cysts during renal ultrasound. The current guidelines provide clinicians the recommendations for genetic testing in children with a positive family history. Given that the vast majority of children with ADPKD present with normal or supra-normal kidney function, we explored the glomerular filtration rates dynamics and the renal ultrasound-adjusted percentiles. In total, 14 out of 16 patients had kidney percentiles over 90%. The gene mutations were equally distributed among our cohort. In addition, we compared the modified Schwartz formula to the quadratic equation after adjusting the serum creatinine measurements. It seems that even though children with ADPKD have enlarged kidneys, the renal function is more likely normal or near normal when the quadratic estimation of glomerular filtration rate is used (qGFR tended to be lower, 111.95 ± 12.43 mL/min/1.73 m2 when compared to Schwartz eGFR 126.28 ± 33.07 mL/min/1.73 m2, p = 0.14). Also, when the quadratic equation was employed, not even a single patient reached the glomerular hyperfiltration threshold. The quadratic formula showed that glomerular filtration rates are linear or slightly decreasing after 1 year of follow-up (quadratic ΔeGFR = −0.32 ± 5.78 mL/min/1.73 m2), as opposed to the Schwartz formula that can falsely classify children in a hyperfiltration state (ΔeGFR = 7.51 ± 19.46 mL/min/1.73 m2), p = 0.019.

In this article, a quadrature formula of degree 2 is given that has degree of exactness 3 and order 5. The formula is valid for any planar curve given in parametric form unlike existing Gaussian quadrature formulas that are valid only for functions.