Standard Squares Research Articles

Low-speed skid resistance performance evaluation of airport runway pavements

ABSTRACT When skid resistance is found inadequate on an airport runway pavement, both high-speed and low-speed skid resistance characteristics of the pavement will have to be examined to determine the actual cause of the problem. Unfortunately, the widely used low-speed skid resistance measuring device, namely British Pendulum Tester (BPT), is not suitable for testing grooved pavements which are a common form of runway pavement construction. To solve the limitations of BPT, a Walking Friction Tester (WFT) was developed to test the low-speed skid resistance performance of airport runway pavements. Laboratory skid resistance tests using BPT and WFT were conducted on asphalt and concrete specimens, five of which were textured with standard square grooves and trapezoidal grooves. It was found that WFT produced more consistent measurements than BPT with smaller coefficient of variation values. Further tests were performed to examine the variability of WFT test results with respect to walking speed and water film thickness respectively. It was found that WFT test results were not affected by changes in walking speeds of operators and water film thickness. Therefore, it can be concluded that WFT is a better method for low-speed skid resistance evaluation of runway pavement.

Bounds on soft rectangle packing ratios

We examine rectangle packing problems where only the areas a1,…,an of the rectangles to be packed are given while their aspect ratios may be chosen from a given interval [1γ,γ]. In particular, we ask for the smallest possible size of a rectangle R such that, under these constraints, any collection a1,…,an of rectangle areas of total size 1 can be packed into R. As for standard square packing problems, which are contained as a special case for γ=1, this question leads us to three different answers, depending on whether the aspect ratio of R is given or whether we may choose it either with or without knowing the areas a1,…,an. Generalizing known results for square packing problems, we provide upper and lower bounds for the size of R with respect to all three variants of the problem, which are tight at least for larger values of γ. Moreover, we show how to improve these bounds on the size of R if we restrict ourselves to instances where the largest element in a1,…,an is bounded.

RETINAL AGING IN COMPANION DOGS

Abstract Companion dogs cohabit with humans in approximately 45% of US households. They experience similar environmental exposures and lifestyles to their human companions, and have shown sensory, cognitive, and neurological decline with aging. The relationship between age and retinal neurologic function in dogs has not been described. The aim of this study was to determine associations between age and retinal full-field electroretinographic measures in companion dogs, an important translational model species for human neurologic aging. Healthy adult companion dogs with no ophthalmic abnormalities were included (n=54, 18 male, 36 female, median weight 25.7kg, median age 89 months). Unilateral full-field light-adapted and dark-adapted electroretinography (ERG) was performed using a handheld device, with mydriasis and topical anesthesia. Standard least squares effect leverage models were used with log transformed data to determine the cross-sectional effect of age, sex, and bodyweight on ERG amplitudes and peak times. Age and sex were significantly associated with ERG outcome variables, more consistently with ERG amplitude than peak time; age had the largest and most significant effect leverage on outcomes (significantly affecting 3/9 peak time and 8/10 amplitude outcome variables). Younger and female dogs had higher ERG amplitudes. Body weight had no significant effect on any outcome. Our finding that aged companion dogs have reduced ERG amplitudes and prolonged peak times mirror ERG findings in aging humans. Because dogs have a shorter lifespan compared with humans, they may act as a sentinel species to monitor for emerging risk factors for age-related neurologic decline.

The welfare of Ghanaian women in trade: the role of English and French language literacy

PurposeThe study aims to assess the effect of English and French language literacy on the welfare of Ghanaian women in trade. Also, this study analyses the geographical variations of such effects from rural to urban areas.Design/methodology/approachUsing the latest living standards survey data, the standard two-stage least squares instrumental variable approach was used to estimate the causal effects.FindingsThe results show that Ghanaian women in trade who are both English and French literate or only English literate are able to improve their welfare significantly relative to their fellows who are illiterate in both English and French or only English, whilst those who are solely French literate do not experience any significant improvement in welfare from trade compared with their counterparts. From the heterogeneous analysis, the findings indicate that the effect is significantly concentrated amongst rural traders but insignificant amongst urban traders.Practical implicationsThe findings of this study inform government and policymakers to consider the effectiveness of the free senior high school (SHS) education policy in improving English and French language literacy and the welfare of women in Ghana. It also informs educational institutions on the importance of adult education in English and French, especially amongst women.Originality/valueThe study quantitatively estimates the effect of English and French language literacy on the welfare of Ghanaian women in trade by employing an instrumental variable approach to assess the causal effect. Uniquely, the study finds that language literacy is a significant tool in improving the welfare of rural women engaged in trade in Ghana.

Higher Order Partial Least Squares Path Modeling Using Binary Data: An Application on Multidimensional Poverty and Social Protection in East Java Province

The standard partial least squares path modeling (PLS-PM) estimation process assumes the observed data as continuous variables. With slight modifications, this estimation algorithm can be used for data on a binary scale and even for more complex models such as higher order constructs. This study aims to determine by simulation and application of real data the performance of the higher-order construct modeling approach, which of the repeated indicator and two-stage approaches provides better results. From simulation study it was found that the repeated indicator approach with binary data (BinPLS) was better than the two-stage approach. Empirical results also show that the BinPLS measurement model with the repeated indicator approach is better than standard PLS. Evaluation of the structural model also shows that BinPLS with a repeated indicator approach is the best because it produces path coefficients and the power to explain multidimensional poverty and social protection models that are better than BinPLS with a two-stage approach and standard PLS.

Craving dynamics and related cerebral substrates predict timing of use in alcohol, tobacco, and cannabis use disorders

BackgroundPatients treated for Substance Use Disorders exhibit highly fluctuating patterns of craving that could reveal novel prognostic markers of use. Accordingly, we 1) measured fluctuations within intensively repeated measures of craving and 2) linked fluctuations of craving to connectivity indices within resting-state (rs) brain regions to assess their relation to use among patients undergoing treatment for Alcohol, Tobacco and Cannabis Use Disorders MethodParticipants —64 individuals with SUD for tobacco, alcohol, or cannabis and 35 healthy controls— completed a week of Ecological Momentary Assessment (EMA) during which they reported craving intensity and substance use five times daily. Before EMA, a subsample of 50 patients, and 34 healthy controls also completed resting-state (rs)-MRI acquisitions. Craving temporal dynamics within each day were characterized using Standard Deviation (SD), Auto-Correlation Factor (ACF), and Mean Successive Square Difference (MSSD). Absolute Difference (AD) in craving between assessments was a prospective prediction measure. ResultsWithin-day, higher MSSD predicted greater substance use while controlling for mean craving. Prospectively higher AD predicted later increased substance use independently of previous use or craving level. Moreover, MSSD was linked to strength in five functional neural connections, most involving frontotemporal systems. Cerebello-thalamic and thalamo-frontal connectivity were also linked to substance use and distinguished the SUD from the controls. ConclusionTo the best of our knowledge, this is the first study to indicate that instability in craving may be a trigger for use in several SUD types, beyond the known effect of craving intensity.

Numerical Simulation on Wind Speed Amplification of High-Rise Buildings with Openings

To explore the influence of openings on wind loads and wind speeds in high-rise buildings, the wind flow around three-dimensional (3D) square cylinders with a breadth/height aspect ratio of 1:6 was numerically simulated using the large eddy simulation (LES) method via the Fluent 15.0 platform. The opening measures in the X-direction, Y-direction and both directions were all taken into consideration. Firstly, the inflow turbulence synthesis method and parameter settings for LES were verified by comparing the simulation results of standard square cylinders with those of wind tunnel experiments, and the optimal boundary conditions were determined. Then, the wind speed was extracted and compared with the mean wind speed of incoming flow at the same height to analyze the influence of different opening measures on the wind speed of incoming flow by setting monitoring points in the open holes. Finally, the mechanism underlying the effect of the opening form on wind loads and wind speeds was analyzed from the perspective of time-averaged and transient flow field. The results show that the X-direction openings affect the magnitude and distribution of the surface wind pressures by changing the flow separation and flow reattachment. The narrow tube effect can significantly increase the wind speed, while the Y-direction openings have no obvious improvement effect on the surface wind pressures of the structure. The wind speeds in the open holes are greatly reduced due to the shielding effect, and the wind pressures are also reduced for the Y-direction openings. In the X-direction opening holes, the wind speed at the monitoring point increases, while it decreases in the crosswind open holes. In general, the measure of openings in the X-direction can greatly improve the wind load of the structure compared to openings in the Y-direction, and it can provide a good reference for wind power generation in high-rise buildings.

Characteristics and Outcomes of Obstetric Sepsis by Three Sets of Clinical Diagnostic Criteria: A Retrospective Study.

Pregnancy-related mortality in the United States is the highest of all developed nations with a reported rate of 17 deaths per 100,000 live births in 2014 to 2017. Sepsis-related mortality is a major component of pregnancy-related mortality. Similar to nonpregnancy-related sepsis, the criteria for pregnancy-related sepsis are evolving. The purposes of this study were to compare three criteria for sepsis (Sepsis-2, Sepsis-3, California Maternal Quality Care Collaborative [CMQCC]) with one another and to determine patient outcomes using those three sets of criteria. Using the electronic medical record, we obtained granular data on all patients at University of Michigan Medical Center from July 10, 2009 to September 4, 2019 with suspected sepsis (blood cultures and administration of antibiotics) during pregnancy until the 42nd postpartum day. Agreement between the three criteria were assessed with kappa and shown by a Venn diagram. Groups were compared using standardized differences and chi square, rank sum, or independent t-tests. Of the 228 patients having sepsis by any criteria, 191 (83%) patients met the criteria for Sepsis-2, 131 (57%) for Sepsis-3, and 62 (27%) met criteria according to CMQCC. Agreement between the three criteria ranged from kappa = 0.13 (95% confidence interval [CI]: 0.09, 0.18) to kappa = 0.31 (95% CI: 0.23, 0.39). Patients who met CMQCC criteria tended to have more comorbidities and higher APACHE II (Acute Physiology And Chronic Health Evaluation) scores. Mortality (by 90 days) among the groups was low with 10 (4%) patients dying. Patients meeting criteria for CMQCC sepsis had higher mortality than the non-CMQCC patients with sepsis (10 vs. 2%, standardized difference = 0.31, p = 0.027). The agreement among Sepsis-2, Sepsis-3, and CMQCC diagnostic criteria is weak. CMQCC criteria identifies patients with sepsis at higher risk of death. · Agreements (kappa) between the three criteria are poor.. · CMQCC sepsis patients have more comorbidities.. · Endometritis was the most common cause of sepsis.. · CMQCC mortality was 10%; non-CMQCC mortality was 2%..

Working capital policy of newly incorporated firms

PurposeThe present study examines the initial working capital policy (WCP) and its evolution for newly established manufacturing firms.Design/methodology/approachUsing panel data of 162 firms over a period of 10 years, the study analyses the persistence-cum-convergence in WCP over the subsequent years through descriptive analysis and difference of means test. Further, the prevalence of ß – convergence, and σ-convergence has been examined using standard least squares regression, dynamic panel analysis and the Wald test.FindingsThe results indicate that sample firms continue to follow the initial WCP in the subsequent years with a gradual convergence in the WCP. Alternatively, the firms with aggressive (conservative) WCP at the time of incorporation will continue following it. Further, the firms with aggressive initial WCP have witnessed higher growth than those with conservative initial WCP.Research limitations/implicationsFindings will assist managers and practitioners to understand the dynamics of WCP over the life cycle of the firm and select appropriate WCP as certain policies lead to certain growth paths.Originality/valueThough working capital management has been recognized as a critical managerial decision, limited research is available on its evolution, especially for newly established manufacturing companies in an emerging economy. Current research attempts to fill this gap and provide valuable insights for the effective management of liquidity.

Multivariate Weighted Total Least Squares Based on the Standard Least-Squares Theory

The weighted total least squares (WTLS) has been widely used in many geodetic problems to solve the error-in-variable (EIV) models in which both the observation vector and the design matrix contain random errors. This method is widely applied in its univariate form, where the observations and unknown coefficients appear in vector forms. However, in some geodetic problems, data sets appear in more than one dimension, and the vector representation of the univariate model may not be suitable to efficiently solve the problem. The observation and unknown parameter vectors can then be replaced with their counterparts in matrix representations in a multivariate model. In this paper, we propose a simple, fast, and flexible procedure for solving the multivariate WTLS (MWTLS) problem using the standard least squares theory. The method has the capability of applying to large-size and high-dimensional data sets. Our numerical experiments on both simulated and real datasets demonstrate the high performance of the proposed method for solving multivariate WTLS problems. In terms of computational complexity, our method outperforms the existing state-of-the-art methods, both numerically and analytically.

An analytical solution for friction coefficients of grooved pavements considering tire rubber-groove interaction

To reduce the loss of skid resistance of pavement in wet weather, pavement grooving is used to improve aircraft operation safety on runways. This study presents an analytical solution to analyze mechanical interactions between tire tread rubber and pavement surface grooves for calculating friction coefficients of aircraft tires on runway pavements. The energy dissipation theory is utilized to calculate the contribution of rubber-groove interlock and the friction on plane part of pavement surface due to surface texture is accounted using Brush model. The comparison of model results and field measurements proves the capability of the proposed method to predict friction coefficients of aircraft tire on runway pavements with various groove configurations. The evaluation of trapezoidal grooved pavement shows similar friction coefficients compared to the standard square grooved pavement regulated by the Federal Aviation Administration (FAA). The friction coefficients of grooved pavement vary depending on the inclined angles of groove and edge-to-edge spacing that are two important geometry parameters. The findings demonstrate the pronounced influences of rubber deposits and groove deterioration on skid resistance of runway pavements. The analysis results can be further used to design optimized groove configuration and determine maintenance threshold for safe operation of aircraft on runways.

PSIV-18 Live Yeast (Saccharomyces Cerevisiae) Improves Body Condition Score and Reduces Rectal Temperature in Sows at Weaning

Abstract Achieving optimal health of the sow during gestation and lactation is important to ensure sow longevity and piglet performance. As an oxygen scavenger, live yeast suppresses the growth of undesirable bacteria and promotes fiber-degrading microbes. Consequently, yeast has the potential to promote a healthy gut microbiome and support immune status. Therefore, the objective of this study was to evaluate the effects of live yeast supplementation on sow performance during gestation and lactation. A total of 40 sows (Landrace × Yorkshire) were assigned to two dietary treatments based on parity and expected farrowing date. The two dietary treatments consisted of a basal diet without (control) or with supplementation of live yeast (Vistacell, AB Vista, UK). Gestation diets were fed for 4-weeks pre-farrowing with the live yeast treatment included at 0.5 kg/t. Lactation diets were fed from farrow until weaning at approximately 24 days with live yeast treatment included at 1.0 kg/t. Data were analyzed by ANOVA using the standard least squares option of the fit model platform in JMP 16.0 Pro. Treatment differences were deemed significant at P < 0.05. At farrowing, sows had comparable body weights, backfat thickness, muscle depth, rectal temperature (rTEMP) and body condition score (BCS), irrespective of treatment. At weaning, sows supplemented with live yeast had a greater BCS (3.4 vs. 3.0) than non-supplemented sows (P < 0.01). As average daily feed intakes were comparable across treatments, this suggests that live yeast fed sows were better able to retain condition during the lactation period. In addition, rTEMP was lower (38.6°C vs 39.1°C) in sows fed live yeast at the end of lactation compared with non-supplemented sows (P < 0.05). Although rTEMP was considered within the safe range for sows post-farrow, lowering rTEMP with live yeast may indicate health benefits to the sow. These findings demonstrate the potential of live yeast to improve body condition and reduce the risk of vulnerable sows at weaning.

The effect of green culture and identity on organizational commitment

When effectively implemented, green management practices greatly influence environmental damage and offer intra-organizational advantages, leading to good environmental consequences and substantial organizational benefits. The effect of green organizational culture (GOC) and identity (GOI) on organizational commitment (OC) through the mediating role of job satisfaction (JS) has been investigated in this study, considering the need to identify intra-organizational variables to adopt environmental policies. This study analyzed environmental pollution in Isfahan province, focusing on employees of 56 Iranian manufacturing companies. Data were collected using standard questionnaires and Partial least squares structural equation modelling via SmartPLS. Results showed that the variables of GOC and GOI significantly impacted OC through the mediating role of JS. This study interprets that green organizational approaches can strengthen and increase commitment, creating a positive collective and individual perspective toward organizations. Successful implementation of GOC and GOI encourages other organizations to achieve similar benefits, leading to better environmental performance.

Parental Perception of Remote Education in Pandemic: An Analysis Based on Children's Cognitive Performance.

The COVID-19 pandemic significantly changed patterns of human interaction, including in the educational sector, which was forced to transform relationships among students, families, and the academic community. The present study sought to establish the interrelationships between performance on cognitive tests during the preschool stage and the perceptions of parents about remote education in school children during the pandemic. The study included 100 preschool children from socially vulnerable sectors who underwent remote and distance learning in 2020 and 2021. The reliability of the applied questionnaire was determined through a confirmatory factor analysis. A structural equation model was constructed to determine the perceptions of parents about remote education based on cognitive performance during the preschool stage. The model fit yielded favorable results for predictive variables (χ2 = 7.734, DF = 9 [p = 0.561], the comparative goodness-of-fit index [CFI] = 1.000, root mean square error of approximation [RMSEA] = 0.000, standardized mean square residual [SRMR] = 0.069), and executive function (χ2 = 3.711, DF = 5 [p > 0.592], CFI = 1.000, RMSEA = 0.000, SRMR = 0.039) as latent variables that affected parents' perceptions. These results indicate that parents' perceptions of remote education are mediated by predictive aspects of learning and executive function during the preschool stage.

Tourism and the Mediterranean Experience Amidst Environmental Issues: Fresh Insights from Panel Analysis

According to the United Nations World Tourism Organization (UNWTO), tourism is critical to a country's economic development. It acts as a catalyst for direct and indirect job creation, economic growth, and the attraction of foreign direct investment (FDI). To this end, the present study looks into the relationship between economic growth (GDP), domestic credit (DC), tourism (TR), FDI, and CO2 emissions for selected Mediterranean countries. This study employs panel corrected standard errors (PCSE) and dynamic ordinary least squares (DOLS) approaches to assure the trustworthiness of the findings. The empirical information gathered supports the idea that tourism adds to pollution in the analyzed blocs. Furthermore, the data supports the pollution haven hypothesis concept by demonstrating that an increase in FDI harms the environment. The study's findings advocate for precautionary actions to alleviate the detrimental effects of tourism-related pollution. Ecotourism policies that support sustainable behaviors must be developed and implemented. Countries can establish a balance between economic growth and environmental protection by implementing such policies. Governments, policymakers, and stakeholders must work together to create effective frameworks and policies that promote responsible tourism. This research fills a knowledge vacuum by shedding light on the specific dynamics of Mediterranean tourism businesses. Economic growth, domestic credit, tourism, FDI, and CO2 emissions are all linked, according to empirical research. The findings highlight the importance of establishing ecotourism legislation and constructing sustainable infrastructure to reduce tourism's negative environmental impacts. Countries may safeguard the long-term viability of their tourism businesses by finding a balance between economic growth and environmental protection.

Fused robust geometric nonparallel hyperplane support vector machine for pattern classification

Recently, introducing nonconvex loss functions in support vector machine (SVM) to improve the robustness against varies noises has been drawing much attention. In this paper, we first construct a new robust capped asymmetric elastic net (CaEN) loss function. Second, we describe a novel robust Huberized kernel-based (HK) loss function and theoretically demonstrate several important properties, such as smoothness, boundness and the trade-off between the standard least squares and the truncated least squares. Finally, we apply the CaEN loss and the HK loss into elastic net nonparallel hyperplane SVM (ENNHSVM) to develop a fused robust geometric nonparallel SVM (FRGNHSVM). The proposed FRGNHSVM not only inherits the advantages of ENNHSVM but also improves the robustness of classification problems. An efficient Pegasos-based DC (difference of convex functions) algorithm is implemented to solve the FRGNHSVM optimization problem. In comparison with four famous SVMs, including Lagrangian SVM, twin SVM, pinball SVM and C-loss twin SVM, experimental results on simulations and twelve UCI datasets show that the proposed FRGNHSVM can often improve more than 5% average prediction accuracy. Moreover, the performance of the high prediction accuracy of FRGHNSVM is more significant along with the ratio of label noise increasing, indicating its superiority in dealing with label-contaminated datasets.

Influence of natural resources and infrastructure on travel intention to Tikus Island, Indonesia

Business opportunities in the field of marine tourism on Tikus Island are very potential. So it is important to analyze how the intention of visitors in traveling to Tikus Island is to describe business opportunities and business opportunity strategies. Intentions show how interested visitors are and how infrastructure and resource factors influence it. So that business opportunities can be analyzed from the factors forming the intensity of tourism on Tikus Island. The research was conducted in the city of Bengkulu, namely the coastal pier for the Tikus Island. The research location was chosen purposively because this location is a gathering place for visitors who will go to the Tikus Island. The sampling method is based on accidental sampling. Respondents in this study were those who have visited or will visit Tikus Island. The number of research respondents was 100 people according to the standard analysis tool Model-Partial Least Square analysis (SEM-PLS). The sampling method is based on accidental sampling. Based on the results of data processing, it was found that infrastructure and natural resourcess has a significant effect on travel intention to Tikus Island. Exploring small Islands through marine tourism involves traveling to areas that are still natural and largely unpolluted or disturbed. The entire infrastructure must be prepared in the framework of tourism development. Infrastructure development needs to start right away. This is due to the fact that infrastructure is crucial to company continuity. The presence of complete facilities can affect visitor satisfaction.

Synchrotron X-ray diffraction and radiography - Lattice strain characterization in thin-walled carbon fibre channel structures subjected to buckling

Carbon fibre composites are widely used in low specific stiffness and high strength structures such as airframes. Compressive loading of these assemblies can lead to buckling and localised deformation around defects and imperfections that can hinder performance and lead to overengineering via excessive safety factors. Synchrotron X-Ray Diffraction (SXRD) has recently been shown to be capable of performing lattice strain mapping within carbon fibre composites at the microscale, a previously unprecedented resolution. In this study SXRD and radiography was performed on carbon fibre composite columns produced via two different methods (standard lamination and half square) at a range of different load states: unbuckled, one-third of the buckling load and post buckling. The results provide quantitative insights into the impact of these different production methods on lattice strain and fibre orientation, as well as the influence these factors have on reducing buckling load (by up to 22%). As well as being the first use of SXRD on industrially representative full-size carbon fibre samples, these insights provide invaluable detail into the factors which limit performance and the origins of column failure; crucial factors required to optimise structural design, production and loading capability.

Three-dimensional power sparse code division non-orthogonal multiple access scheme with constellation pair mapping.

This paper proposes a three-dimensional power sparse code division non-orthogonal multiple access (3D-PSCD-NOMA) scheme with 3D constellation pair mapping. The proposed sparse code is based on a balanced incomplete block design (BIBD). Its correlation matrix performs the overall signal mapping of multi-user information. Power multiplexing is realized by overlaying multi-level power signals with different path losses through pair mapping. Compared with the conventional 2D standard square 32 Quadrature Amplitude Modulation (QAM), the proposed 3D constellation pair mapping can improve the constellation points' minimum Euclidean distance (MED) by 17.7%, which is beneficial for the performance of the system. Based on obtaining the optimal power distribution ratio (PDR) for different schemes, a 3D-PSCD-NOMA signal with a rate of 15.22 Gb/s over a 25 km single-mode fiber (SMF) is experimentally performed. The experimental results show that 3D-PSCD-NOMA has a clear superiority. At the same rate, 3D-PSCD-NOMA2 can obtain a sensitivity gain of about 1.6 dB and 1.9 dB over the conventional 2D constellation. Moreover, 3D-PSCD-NOMA reduces the system's peak-to-average power ratio (PAPR) by 1.3 dB. The difference in sensitivity of the system before and after sparse code is about 0.15 dB, and no significant degradation occurred. Due to its advantages in transmission performance, 3D-PSCD-NOMA is a potential solution for future optical access systems.

High-order Accurate Beam Models Based on Discontinuous Galerkin Methods

A novel high-order accurate approach to the analysis of beam structures with bulk and thin-walled cross-sections is presented. The approach is based on the use of a variable-order polynomial expansion of the displacement field throughout both the beam cross-section and the length of the beam elements. The corresponding weak formulation is derived using the symmetric Interior Penalty discontinuous Galerkin method, whereby the continuity of the solution at the interface between contiguous elements as well as the application of the boundary conditions is weakly enforced by suitably defined boundary terms. The accuracy and the flexibility of the proposed approach are assessed by modeling slender and short beams with standard square cross-sections and airfoil-shaped thin-walled cross-sections subjected to bending, torsional and aerodynamic loads. The comparison between the obtained numerical results and those available in the literature or computed using a standard finite-element method shows that the present method allows recovering three-dimensional distributions of displacement and stress fields using a significantly reduced number of degrees of freedom.