Multivariate Formula Research Articles

Influence and Predictive Value of Optional Parameters in New-generation IOL Formulae.

To evaluate the accuracy of various variations of new-generation multivariate intraocular lens (IOL) power calculation using the Barrett Universal II, Castrop, EVO 2.0, Hill-RBF 3.0, Kane, and PEARL-DGS formulae with and without optional biometric parameters. Tertiary care academic medical center. retrospective case series. ology: Single-center study. Inclusion of patients after uneventful cataract surgery implanting AU00T0 IOLs. Data from one single eye per patient were randomly included. Eyes with a best-corrected visual acuity worse than 0.1 logMAR were excluded. IOLCON-optimized constants were used for all formulae other than the Castrop formula. The outcome measures were prediction error (PE) and absolute prediction error (absPE) for the 6 study formulae. 251 eyes from 251 patients were assessed. Excluding lens thickness (LT) led to statistically significant differences in absPE in several formulae. Leaving out horizontal corneal diameter impacted absPE in several formulae . Differences in PE offset were observed between the various formula variations. When using multivariable formulae with an A-constant, including certain optional parameters is vital for optimal refractive results. Formula variations excluding certain biometric parameters need specifically optimized constants and do not perform similarly when using the constant of the respective formula using all parameters.

Prediction of total corneal power in keratoconus using anterior surface data

ABSTRACT Clinical relevance Keratoconus results in an increase in anterior and posterior curvatures and a reduction in corneal thickness. Anterior corneal ectasia is partially compensated by remodelling the corneal epithelium. Therefore, there is an alteration in the relationship between corneal surfaces and variation in corneal power. The variation in corneal power is one of the sources that induces errors in IOL power calculation. Background This study aimed to assess a method for predicting total corneal power in keratoconus using several anterior surface parameters at 3 mm and 4 mm. Methods Tomographic data obtained using Pentacam (Oculus, Germany) were analysed from 280 eyes of 140 patients with keratoconus using anterior and posterior keratometry, anterior Q-value at 8 mm, central corneal thickness, Kmax location and value, and true net power at 4 mm (TNP). Calculated total corneal power (TCPc) at 3 mm was obtained using the Gauss formula. Predicted total corneal power at 3 mm (TCPp3) and 4 mm (TCPp4) was obtained from univariate (TCPp3u and TCPp4u) and multivariate linear regression formulae (TCPp3m and TCPp4m). SimK, anterior Q-value, vertical location, and Kmax value were used in the multivariate formulae. Mean absolute error (MAE) and median absolute error (MedAE) were also calculated. Absolute frequencies within dioptric ranges of all formulas divided for keratoconus grading were evaluated. Results TCPc and TNP exhibited a good correlation (R2 = 0.58, p < 0.05) with a higher dispersion above 50 D of corneal power. Highly significant correlations were observed between TCPp3u and TCPc (R2 = 0.978, p < 0.05) and TCPp3m and TCPc (R2 = 0.989, p < 0.05). Lower but significant correlations were observed between TCPp4u and TNP (R2 = 0.692, p < 0.05) and between TCPp4m and TNP (R2 = 0.887, p < 0.05). The best results for TCP prediction at 3 and 4 mm were obtained with TCPp3m and TCPp4m as follows: MAE of TCPp3m was 0.24 ± 0.20 (SD) D with MedAE of 0.20 D, while MAE of TCPp4m was 0.96 ± 0.77 D with MedAE of 0.80 D. The 3 mm multivariate regression formula results in higher absolute frequencies of prediction errors in the total eyes within 0.5 D (93%) than the univariate formula (81%). At 4mm, the multivariate regression formula has a lower percentage within 0.5 D (32%) than the univariate formula (41%), but the percentage of the multivariate formula is higher within 1 D (63%) than the univariate formula (56%). Conclusion All formulas show a decrease in accuracy with increasing grades of keratoconus. Multivariate linear regression formulae using only anterior surface data can predict TCP with good approximation in eyes with keratoconus in cases where posterior surface parameters are unavailable. The vertical location of Kmax and the anterior asphericity could play a relevant role in the prediction of total corneal power in keratoconus.

Identifying predictive factors for long-term visual recovery after corneal endothelial keratoplasty in Fuchs' dystrophy: Potential interaction between the corneal dysfunction and retinal status.

Descemet membrane endothelial keratoplasty (DMEK) is the main treatment for Fuchs' dystrophy (FECD). The outcomes are excellent, but the final visual recovery may vary from patient to patient with sometimes no obvious reason of such a spread. We conducted a clinical prospective multicentric study to identify the predictive factors for the visual result 1 year after surgery. Eighty three patients (83 eyes) were included. Postoperative BCVA after 1 year was 0.20 ± 0.18 logMAR. Logistic regression revealed that good visual recovery correlated negatively with preoperative central macular thickness (p < 0.001) and the need for rebubbling (p = 0.05), and positively with preoperative visual acuity (p = 0.009). Multivariate formula to predict the 1-year BCVA has been suggested. Preoperative retinal status seems to be the main predictive factor for long-term visual result after DMEK. Our predictive multivariate model could assist in better informing the patient about the prognosis of the surgery, and in adjusting the therapeutic strategy also, further highlighting the essential collaboration between both cornea and retina subspecialists.

Standard vs total keratometry for intraocular lens power calculation in cataract surgery combined with DMEK

To compare the prediction accuracy of standard keratometry (K) and total keratometry (TK) for intraocular lens (IOL) power calculation in eyes undergoing combined cataract surgery and Descemet membrane endothelial keratoplasty (triple DMEK). Tertiary care academic referral center. Retrospective case series. Review of 83 eyes (63 patients) that underwent triple DMEK between 2019 and 2021. Biometry measurements were obtained using a swept-source optical biometer (IOLMaster 700). 63 eyes were used for statistical analysis. Mean error, mean absolute error (MAE), SD, median absolute error, maximum absolute error, root mean squared prediction error, and the percentage of eyes within prediction errors of ±0.50 diopters (D) and ±1.00 D were calculated for 9 multivariate and third-generation formulas using K and TK values (Barrett Universal II, Yeo EVO 2.0, Cooke K6, Kane, Pearl-DGS, Haigis, Holladay 1, Hoffer Q, and SRK/T). Formulas were additionally tested by using the prediction for an IOL power 1 D below the IOL used (IOLup1D). For all formulas, MAE was lower for K than for TK by an average of 0.21 D. The lowest MAE value observed was 0.67 D for "adjusted" SRK/T using K, and the highest MAE values observed were 1.24 D and 1.24 D for nonadjusted Hoffer Q and Haigis using TK, respectively. Overall, lower MAE values were observed for multivariate formulas and SRK/T. In triple DMEK eyes, the prediction accuracy of K was higher than that of TK. The most accurate formulas were SRK/T and multivariate formulas using K with the IOLup1D adjustment.

MacMahon’s statistics on higher-dimensional partitions

Abstract We study some combinatorial properties of higher-dimensional partitions which generalize plane partitions. We present a natural bijection between d-dimensional partitions and d-dimensional arrays of nonnegative integers. This bijection has a number of important applications. We introduce a statistic on d-dimensional partitions, called the corner-hook volume, whose generating function has the formula of MacMahon’s conjecture. We obtain multivariable formulas whose specializations give analogues of various formulas known for plane partitions. We also introduce higher-dimensional analogues of dual stable Grothendieck polynomials which are quasisymmetric functions and whose specializations enumerate higher-dimensional partitions of a given shape. Finally, we show probabilistic connections with a directed last passage percolation model in $\mathbb {Z}^d$ .

Multivariable Technique for the Evaluation of the Trans-stenotic Pressure Gradient.

This study establishes a reliable image-based multivariable technique for measuring the trans-stenotic pressure gradient. A self-made in vitro steady flow model based on adjustable velocities and stenotic properties were used as the experimental subject. The pre-stenotic flow velocity, severity, and length of the stenosis were used as the input variables. Based on equations used to fit the plots of the physically measured pressure gradient values versus each input variable, a multivariable formula for the pressure gradient measurement could then be derived. The flow model was scanned using velocity-encoded phase-contrast magnetic resonance imaging (PC-MRI) to validate the derived formula while simultaneously measuring the trans-stenotic pressure gradient. The correlation between the physically-measured pressure gradient values and the pressure gradient values calculated using the new formula were subsequently analyzed. The results of linear regression analysis using the physically measured pressure gradient values for the new method were compared to values obtained using the simplified Bernoulli equation (R2, 0.991, and 0.975, respectively). In a paired t-test, no statistically significant difference was found between the new method and the physical measurements. The derived multivariable technique was found to reliably measure the trans-stenotic pressure gradient, with better performance than a traditional procedure based on the simplified Bernoulli equation.

Prenatal prediction of very late onset small-for-gestational age newborns in low-risk pregnancies

Prompt identification and correct management of late onset small-for-gestational age newborns can reduce perinatal morbidity and mortality. Given the limitations of current monitoring methods, additional strategies are needed. Besides ultrasound to monitor fetal growth, third trimester Doppler and serum measurement of angiogenic biomarkers, such as soluble fms-like tyrosine kinase-1 and placental growth factor, have been proposed as promising predictors of late onset small-for-gestational age fetuses. Objective To find a multivariate model for predicting small-for-gestational age newborns at 36 weeks’ gestation by using clinical, biochemical and ultrasound measurements. Materials and Methods We evaluated 564 low-risk pregnant women and recorded maternal age, maternal body mass index, maternal mean blood pressure, soluble fms-like tyrosine kinase-1 (multiples of the median), placental growth factor (multiples of the median), soluble fms-like tyrosine kinase-1/placental growth factor ratio, estimated fetal weight centile and mean uterine artery pulsatility index at 36 weeks. Binary logistic regression was used. Statistical significance was set at 95% level (p < 0.05). Results We found three multivariate models showing relatively small differences in predictive capability. Model 1 only included estimated fetal weight centiles (area under the curve [AUC] 0.86; R2 = 0.42; p < 0.0001), Model 2 estimated fetal weight centiles and placental growth factor (multiples of the median) (AUC 0.87; R2 = 0.44; p < 0.0001) and Model 3 estimated fetal weight centiles, placental growth factor (multiples of the median) and mean uterine artery pulsatility index (AUC 0.88; R2 = 0.45; p < 0.0001). Conclusion Small-for-gestational age at delivery may be predicted by using a multivariate formula. The inclusion of parameters other than estimated fetal weight centile at 36 weeks’ gestation modestly improves the predictive capability of the model. Clinical decisions should consider whether or not these slight differences deserve a change in current strategies.

Hybrid model combining multivariate regression and machine learning for the rapid prediction of interior temperatures affected by thermal diodes and solar cavities

Sustainable design often requires highly efficient building performance evaluations. This study proposed a hybrid model combining multivariate regression modelling (MRM) and machine learning modelling (MLM) for the rapid prediction of interior temperatures affected by heat pipe thermal diodes and solar cavities based on experimental data. A heat pipe thermal diode can promote unidirectional heat transmission from the solar cavity on the south side of our newly built experimental house to the indoor environment to increase the interior temperature and reduce the heating load in cold climates. Experimental data were collected and then imported, cleaned, and split according to MRM and MLM requirements, respectively. In MRM, linear multivariate formulas were generated according to the thermal diode's two different working conditions. In MLM, a machine-learning model was created and trained using the experimental data. The results our hybrid model produced were comprehensively evaluated via R-square, statistical discrepancies, and complex MRM analyses. The similarity between the prediction and experimental results clearly demonstrates our model's accuracy and efficiency. This research was an original attempt to integrate emerging computational tools and provide a means to perform highly efficient quantitative analysis of indoor thermal environments for environmental studies and sustainable designs in the early stages.

Predicting the individual probability of macular hole closure following intravitreal ocriplasmin injections for vitreomacular traction release using baseline characteristics

The primary objective was to create and establish a new formula that predicts the individual probability of macular hole closure for eyes with full thickness macular holes (FTMH) accompanied by vitreomacular traction (VMT) which received enzymatic vitreolysis using intravitreally administered ocriplasmin. The secondary objective was to evaluate the forecast reliability of a previously published formula for VMT resolution in VMT-only eyes (OddsIVO-Success = eIntercept × ORyears × ORln(µm); ProbabilityIVO-Success = OddsIVO-Success/(OddsIVO-Success + 1)) on VMT resolution using the current dataset of eyes with FTMH accompanied by VMT. Retrospective analysis of the OASIS, ORBIT, and INJECT-studies. Patients with FTMH and VMT with complete information (n = 213) were included. The effect of gender, age, FTMH diameter, lens status and the presence of epiretinal membranes (ERM) on FTMH closure was assessed using separate univariate logistic regression analyses. With regard to VMT release separate univariate regression analyses were carried out and results were compared with formerly published data of VMT resolution in eyes with VMT only. Overall, 126 eyes (63%) experienced VMT resolution within 28 days. Younger age (p < 0.0001) and VMT diameter (p = 0.041) had a significant impact on VMT release. Overall, 81 eyes (38%) treated with ocriplasmin showed FTMH closure within 28 days. Univariate analysis of the different predictors analyzed revealed that FTMH diameter < 250 µm had a significant impact on treatment success (p = 0.0495). It was not possible to calculate and establish a new multivariate formula that can predict the individual FTMH closure probability for eyes with FTMHs and VMT. However, the results of VMT release prediction in eyes with FTMHs accompanied by VMT matched the prediction of VMT release in eyes with VMT only when using the previously published formula. All in all, predictors for calculating the individual probability of VMT resolution on the one hand and FTMH closure on the other hand are different suggesting diverse pathophysiological mechanisms.

Validation of skeletal muscle mass assessment at the level of the third cervical vertebra in patients with head and neck cancer

BackgroundLow skeletal muscle mass (SMM) is associated with adverse outcomes. SMM is often assessed at the third lumbar vertebra (L3) on abdominal imaging. Abdominal imaging is not routinely performed in patients with head and neck cancer (HNC). We aim to validate SMM measurement at the level of the third cervical vertebra (C3) on head and neck imaging. Material and methodsPatients with pre-treatment whole-body computed tomography (CT) between 2010 and 2018 were included. Cross-sectional muscle area (CSMA) was manually delineated at the level of C3 and L3. Correlation coefficients and intraclass correlation coefficients (ICCs) were calculated. Cohen’s kappa was used to assess the reliability of identifying a patient with low SMM. ResultsTwo hundred patients were included. Correlation between CSMA at the level of C3 and L3 was good (r = 0.75, p < 0.01). Using a multivariate formula to estimate CSMA at L3, including gender, age, and weight, correlation improved (r = 0.82, p < 0.01). The agreement between estimated and actual CSMA at L3 was good (ICC 0.78, p < 0.01). There was moderate agreement in the identification of patients with low SMM based on the estimated lumbar skeletal muscle mass index (LSMI) and actual LSMI (Cohen’s κ: 0.57, 95%CI 0.45–0.69). ConclusionsCSMA at C3 correlates well with CSMA at L3. There is moderate agreement in the identification of patients with low SMM based on the estimated lumbar SMI (based on measurement at C3) and actual LSMI.

Examining the Clinical Utility of Selected Memory-Based Embedded Performance Validity Tests in Neuropsychological Assessment of Patients with Multiple Sclerosis.

Within the neuropsychological assessment, clinicians are responsible for ensuring the validity of obtained cognitive data. As such, increased attention is being paid to performance validity in patients with multiple sclerosis (pwMS). Experts have proposed batteries of neuropsychological tests for use in this population, though none contain recommendations for standalone performance validity tests (PVTs). The California Verbal Learning Test, Second Edition (CVLT-II) and Brief Visuospatial Memory Test, Revised (BVMT-R)—both of which are included in the aforementioned recommended neuropsychological batteries—include previously validated embedded PVTs (which offer some advantages, including expedience and reduced costs), with no prior work exploring their utility in pwMS. The purpose of the present study was to determine the potential clinical utility of embedded PVTs to detect the signal of non-credibility as operationally defined by below criterion standalone PVT performance. One hundred thirty-three (133) patients (M age = 48.28; 76.7% women; 85.0% White) with MS were referred for neuropsychological assessment at a large, Midwestern academic medical center. Patients were placed into “credible” (n = 100) or “noncredible” (n = 33) groups based on a standalone PVT criterion. Classification statistics for four CVLT-II and BVMT-R PVTs of interest in isolation were poor (AUCs = 0.58–0.62). Several arithmetic and logistic regression-derived multivariate formulas were calculated, all of which similarly demonstrated poor discriminability (AUCs = 0.61–0.64). Although embedded PVTs may arguably maximize efficiency and minimize test burden in pwMS, common ones in the CVLT-II and BVMT-R may not be psychometrically appropriate, sufficiently sensitive, nor substitutable for standalone PVTs in this population. Clinical neuropsychologists who evaluate such patients are encouraged to include standalone PVTs in their assessment batteries to ensure that clinical care conclusions drawn from neuropsychological data are valid.

Lagrange Inversion and Combinatorial Species with Uncountable Color Palette

We prove a multivariate Lagrange-Good formula for functionals of uncountably many variables and investigate its relation with inversion formulas using trees. We clarify the cancellations that take place between the two aforementioned formulas and draw connections with similar approaches in a range of applications.

The Effect of Pharmacological Dilation on Calculation of Targeted and Ideal IOL Power Using Multivariable Formulas.

BackgroundTo examine the effect of pharmacologic dilation on biometric parameters measured by the Lenstar LS 900, and whether these changes affect the power of the calculated intraocular lens (IOL) using multivariable formulas in an undilated versus pharmacologically dilated state.MethodsProspective study of 98 phakic eyes from 53 patients. Axial length (AL), central corneal thickness (CCT), anterior chamber depth (ACD), lens thickness (LT), and keratometry (K) readings were measured. The first set of measurements was taken prior to dilation. After dilation (pupil diameter ≥ 6.0 mm), a second set of measurements was taken. The Barrett, Olsen, Hill-RBF, Haigis, SRK/T, and Holladay I formulas were used to calculate IOL power before and after dilation. Two calculation methods were used: method A used a commonly available IOL targeted to achieve the lowest myopic spheroequivalent residual refraction; method B calculated ideal IOL power for emmetropia.ResultsStatistically significant increases were seen in CCT (p < 0.01), ACD (p < 0.01), and AL (p < 0.01) whereas a statistically significant decrease was seen in LT (p < 0.01) post dilation. Using method A, the percentage of eyes which would have received an IOL with 0.5 D or 1.0 D of higher power, if post-dilation measurements were used, were 25.5%, 30.6%, 20.4%, and 23.5% for Barrett, Olsen, Hill-RBF, and Haigis, respectively. Using method B, only Haigis and Olsen had a statistically significant increase in ideal IOL power.ConclusionsPharmacologic dilation can be associated with an increase in non-custom IOL dioptric power when using multivariable formulas, which may lead to a myopic surprise.

Acoustic Psychometric Severity Index of Dysphonia (APSID): Development and Clinical Application

The purpose of this study was to explore the predictability of the Korean version of the Voice Activity and Participation Profile (K-VAPP) scores and acoustic measures for perceived severity of voice disorders. Furthermore, usefulness of the index derived from the multivariate formula as a screening tool for voice disorders was explored and compared with that of the Cepstral Spectral Index of Dysphonia (CSID). A total of 150 patients with various voice disorders (42 males and 108 females, age=45.15 ± 15.15 years) and matched 50 normal controls (14 males and 36 females, age=44.78 ± 13.70 years), participated in the study. Correlates of perceived overall severity were explored by a stepwise regression analysis with regards to demographic information (age, gender, and professional voice use), jitter, shimmer, and noise-to-harmonic ratio of vowel samples, cepstral peak prominence (CPP), L/H spectral ratio, and their standard deviations of sentence and vowel samples, and psychometric measures of the K-VAPP. Using the ROC curve analysis, the area under curve (AUC) of the novel index derived from the regression equation and the CSID were compared and the cut-off score of the index was obtained. A significant portion (adjusted R square=79.0%) of the overall severity perceived by clinicians was predicted by five parameters: CPP of the sentence and vowel production, the self-perceived severity subscale score of the K-VAPP, σCPP of the vowel production, and gender. The AUC of the novel index was 0.935 (95% confidence interval 0.891-0.965) and significantly higher than that of the CSID of vowel samples (AUC=0.832). The cutoff score with the highest Youden J Index (0.7612) was >22.257617 (sensitivity=82.12%, specificity=94.00%). The current data showed the possibility that a novel index reflecting both acoustic and psychometric correlates of auditory-perceptual estimates for dysphonia severity could be suggested and possibly named as the "Acoustic Psychometric Severity Index of Dysphonia (APSID)." Further studies pertaining to the follow-up of various voice disorders are needed to extend its clinical usefulness.

Arctangent Formulas and Pi

Using both geometrical and analytical approaches, new multivariable formulas connecting the arctangent function and the number π are produced.

Factors That Affect The Event Of Hipertension In Elderly In The Herlang Puskesmas Working Area

According to data from the 2014 Bulukumba health service, there were 6,355 people with hypertension and in 2016 there were 10,430 people and there were 11,714 blood pressure measurements, this hypertension increased every year. The purpose of this study is to know the factors that influence the incidence of hypertension in the elderly. Research design with 'Cross-sectional' 'the population in this study were elderly in the working area of ​​the Herlang Public Health Center many as 120 respondents, the sample in this study amounted to 62 respondents take by using a Multivariate formula, data analysis using the result of this study indicates using the chi-square test with the value (p = 0.027), which men that there is an effect of smoking on the incidence of hypertension. And the consumption of salt with values ​​(p = 0.012), which means there is an influence of salt consumption on the incidence of hypertension and lack of physical activity obtained values ​​(p = 0.012) which means there is an influence on the incidence of hypertension in the elderly. The conclusion of this research is' there is an influence between smoking, consuming salts and lack of physical activity in the working area of ​​the Herlang Public Health Center. It is suggested that the results of this study can be used as scientific reading material in the library and can also be used as reference material for students who examine the problem.

Prediction of endotracheal tube size in children by predicting subglottic diameter using ultrasonographic measurement versus traditional formulas.

Background:Paediatric airway assessment remains the most challenging task before the anaesthesiologists. Recent advancement in ultrasonography techniques should now allow for accurate and descriptive evaluation of paediatric airway. To compare calculated external diameters of the endotracheal tube from physical indices of traditional formulas and predetermined by ultrasound.Materials and Methods:100 subjects of either sex between 12-60 months of age, undergoing various elective surgeries under general anaesthesia requiring endotracheal intubation were enrolled in the study. The transverse diameter was measured at the level of cricoids cartilage by ultrasonography. The tracheal tube was considered best fit if air leak was satisfactory at 15-20 cm H2O of airway pressure. The obtained values were compared with the values of endotracheal tube size calculated by various age, height, weight based formulas and diameter of right and left little finger. The correlation of size of Endotracheal tube by different modalities was done and Pearson's correlation coefficient was obtained.Results:According to Pearson's correlation there was a moderate correlation of best fit Endotracheal tube with endotracheal tube size by age based formula (r = 0.743), body length based formula (r = 0.683), right little finger based formula (r = 0.587), left little finger based formula (r = 0.587) and multivariate formula (r = 0.741). There was a strong correlation with ultrasonography (r = 0.943).Conclusion:Ultrasonography is a reliable method of estimation of subglottic diameter and for prediction of endotracheal tube size in children.

Wideband Absorbance and 226-Hz Tympanometry in the Prediction of Optimal Distortion Product Otoacoustic Emission Primary Tone Levels.

Distortion product otoacoustic emission (DPOAE) amplitude is sensitive to the primary tone level separation effective within the cochlea. Despite potential for middle ear sound transmission characteristics to affect this separation, no primary tone level optimization formula accounts for its influence. This study was conducted to determine if inclusion of ear- and frequency-specific immittance features improves primary tone level optimization formula performance beyond that achieved using a univariate, L2-based formula. For 30 adults with normal hearing, DPOAE, wideband absorbance, and 226-Hz tympanometry measures were completed. A mixed linear modeling technique, incorporating both primary tone and acoustic immittance features, was used to generate a multivariable formula for the middle ear-specific recommendation of primary tone level separations for f2 = 1-6 kHz. The accuracy with which L1OPT, or the L1 observed to maximize DPOAE level for each given L2, could be predicted using the multivariable formula was then compared with that of a traditional, L2-based univariate formula for each individual ear. Use of the multivariable formula L1 = 0.47L2 + 2.40A + f2param + 38 [dB SPL] resulted in significantly more accurate L1OPT predictions than did the univariate formula L1 = 0.49L2 + 41 [dB SPL]. Although average improvement was small, meaningful improvements were identified within individual ears, especially for f2 = 1 and 6 kHz. Incorporation of a wideband absorbance measure into a primary tone level optimization formula resulted in a minor average improvement in L1OPT prediction accuracy when compared with a traditional univariate optimization formula. Further research is needed to identify characteristics of ears that might disproportionately benefit from the additional measure.

Simulating the hydrological performance of low impact development in shallow groundwater via a modified SWMM

Low impact development (LID) practices are effective in restoring natural hydrological processes, but they may be affected by groundwater and pose additional risk to groundwater dynamics and contamination in shallow groundwater conditions. Their performance in shallow groundwater is not well understood due to monitoring difficulty and the deficiency of modeling tools. The Storm Water Management Model (SWMM) is an urban hydrology-hydraulic model that has been widely used to evaluate the performance of LID practices. However, it cannot accurately simulate the hydrological processes of LID practices in shallow groundwater. This study presents the development, calibration, validation, and testing of a modified SWMM (SWMM-LID-GW) that incorporates groundwater feedbacks into LID simulations. The hydrological performance of LID practices under different environmental conditions was simulated, based on which the impacts of initial groundwater table depth, rainfall type, and in-situ soil type were evaluated, and a number of general nonlinear multivariate formulas were proposed to predict the hydrologic performance of LID practices in shallow groundwater environment and support the feasibility analysis of LID practices before project implementation. The reduction of exfiltration and increase of groundwater drainage in shallow groundwater accounted for a significant proportion of the water budget of LID practices. The influence of shallow groundwater was greater for shallower groundwater tables, in less permeable in-situ soils, and for events of higher intensities and longer durations. However, due to the dominant role of shallow groundwater, the impacts of both rainfall type and in-situ soil type on the hydrological performance of LID practices in shallow groundwater were minimal in general, in contrast to the impacts on deep groundwater tables. The SWMM-LID-GW outperformed the current SWMM for a wide range of groundwater conditions, particularly for locations in which the groundwater table frequently rises to 1.0 m or less below ground.

On Functional Equations Characterizing Derivations: Methods and Examples

Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and automorphisms are additive functions satisfying some further functional equations as well. It is an important question that how these morphisms can be characterized among additive mappings in general. The paper contains some multivariate characterizations of higher order derivations. The univariate characterizations are given as consequences by the diagonalization of the multivariate formulas. This method allows us to refine the process of computing the solutions of univariate functional equations of the form $$\begin{aligned} \sum _{k=1}^{n}x^{p_{k}}f_{k}(x^{q_{k}})=0, \end{aligned}$$ where $$p_k$$ and $$q_k$$ ( $$k=1, \ldots , n$$ ) are given nonnegative integers and the unknown functions $$f_{1}, \ldots , f_{n}:R\rightarrow R$$ are supposed to be additive on the ring R. It is illustrated by some explicit examples too. As another application of the multivariate setting we use spectral analysis and spectral synthesis in the space of the additive solutions to prove that it is spanned by differential operators. The results are uniformly based on the investigation of the multivariate version of the functional equations.