Conic Research Articles

High frequency heart rate variability is associated with sensitivity to affective touch

C-tactile afferents (CTs) are a class of unmyelinated, mechanosensitive nerve fibre that respond optimally to skin temperature, slow moving touch typical of a caress. They are hypothesised to signal the rewarding value of affiliative tactile interactions. While CT firing frequency is positively correlated with subjective ratings of touch pleasantness, trait differences in sensitivity to the specific hedonic value of CT targeted touch have been reported.Inter-individual differences in vagally mediated, high frequency heart rate variability (HF-HRV) have been linked to variation in visual social cognition. Thus, the aim of the present study was to examine the relationship between resting state HF-HRV and sensitivity to socially relevant CT targeted touch.58 healthy participants first had a 5-minute electrocardiogram. They then rated the pleasantness of 5 randomly presented velocities of robotically delivered touch. Three velocities fell within (1, 3, 10 cm/s) and two outside (0.3, 30 cm/s) the CT optimal range. Each velocity was delivered twice.On a group level, affective touch ratings were described by a negative quadratic function, with CT optimal velocities rated as more pleasant than slower and faster speeds. Simple regression analysis confirmed participants’ HF-HRV was significantly predicted by the quadratic curve fit of their touch ratings, with higher HF-HRV associated with a better quadratic fit.These findings indicate that, in line with previous observations that higher HF-HRV is associated with enhanced sensitivity to visual social cues, trait differences in autonomic control could account for previously reported individual differences in CT sensitivity.

Dietary supplementation with succinic acid improves growth performance and flesh quality of adult Nile tilapia (Oreochromis niloticus) fed a high-carbohydrate diet

To evaluate the effects of dietary supplementation with succinic acid on growth performance, flesh quality, glucose, and lipid metabolism of Nile tilapia (Oreochromis niloticus) fed a high-carbohydrate diet (HCD), five iso-nitrogenous and iso-lipidic diets were prepared as follows: HCD (control group) consisting of 55% corn starch and HCD supplemented with 0.5%, 1.0%, 2.0%, and 4.0% succinic acid, respectively. Tilapia with an initial body weight of 204.90 ± 1.23 g randomly assigned to 15 tanks with 3 replicates per group and 10 fish per tank fed for 8 weeks. Increasing dietary succinic acid supplementation resulted in significant second-order polynomial relationship in the weight gain rate (WGR), specific growth rate (SGR), feed conversion ratio (FCR), protein efficiency rate (PER), viscerosomatic index, condition factor, and contents of muscular crude lipid and glycogen (P < 0.05). The hepatosomatic index, mesenteric fat index, liver glycogen content and crude lipid contents of the whole-body and liver demonstrated significantly linear and second-order polynomial relationship (P < 0.05). Quadratic curve model analysis based on WGR, SGR, PER, and FCR demonstrated that optimal supplementation with succinic acid in the HCD of Nile tilapia ranged from 1.83% to 2.43%. Fish fed with 1.0% succinic acid had higher muscular hardness, increased the contents of alkali-soluble hydroxyproline in collagen, docosahexaenoic acid (DHA) and n-3 polyunsaturated fatty acid (n-3PUFA) in muscle, and lower total fatty acid content in muscle (P < 0.05) compared with the control group. Compared to the control group, dietary supplementation with 1.0% succinic acid significantly increased the contents of total bounding amino acid (arginine, histidine, isoleucine, lysine, methionine, alanine, proline), total flavor amino acid (free aspartic acid), the catalase (CAT) activity and total antioxidant capacity, and the mRNA relative expression levels of CAT, superoxide dismutase (SOD), and nuclearfactor erythroidderived 2-like 2 (Nrf2) in muscle (P < 0.05). Furthermore, succinic acid supplementation significantly up-regulated mRNA relative expression levels of glycolysis genes (hexokinase 2 [HK2], phosphofructokinase, muscle-A [PFKMA], and phosphofructokinase, muscle-B [PFKMB]), a key glycogen synthesis gene (glycogen synthase [GYS]), and lipid catabolism genes (carnitine palmitoyltransferase-1B [CPT1B], hormone sensitive lipase [HSL], and lipoprotein lipase [LPL]), while down-regulating the mRNA relative expression level of fatty acid synthase (FASN) in muscle (P < 0.05). In conclusion, dietary supplementation with 1.83% to 2.43% succinic acid improved muscle quality by increasing muscle antioxidant capacity and hardness, changing muscle amino acid and fatty acid composition, and regulating muscle glucose and lipid metabolism.

A point-normal interpolatory subdivision scheme preserving conics

The use of subdivision schemes in applied and real-world contexts requires the development of conceptually simple algorithms that can be converted into fast and efficient implementation procedures. In the domain of interpolatory subdivision schemes, there is a demand for developing an algorithm capable of (i) reproducing all types of conic sections whenever the input data (in our case point-normal pairs) are arbitrarily sampled from them, (ii) generating a visually pleasing limit curve without creating unwanted oscillations, and (iii) having the potential to be naturally and easily extended to the bivariate case. In this paper we focus on the construction of an interpolatory subdivision scheme that meets all these conditions simultaneously. At the centre of our construction lies a conic fitting algorithm that requires as few as four point-normal pairs for finding new edge points (and associated normals) in a subdivision step. Several numerical results are included to showcase the validity of our algorithm.

Distinct distances in [formula omitted] between quadratic and orthogonal curves

We study the minimum number of distinct distances between point sets on two curves in R3. Assume that one curve contains m points and the other n points. Our main results:(a) When the curves are conic sections, we characterize all cases where the number of distances is O(m+n). This includes new constructions for points on two parabolas, two ellipses, and one ellipse and one hyperbola. In all other cases, the number of distances is Ω(min{m2/3n2/3,m2,n2}).(b) When the curves are not necessarily algebraic but smooth and contained in perpendicular planes, we characterize all cases where the number of distances is O(m+n). This includes a surprising new construction of non-algebraic curves that involve logarithms. In all other cases, the number of distances is Ω(min{m2/3n2/3,m2,n2}).

Effect of the supplementation of exogenous complex non-starch polysaccharidases on the growth performance, rumen fermentation and microflora of fattening sheep.

The objective of this study was to evaluate the effects of exogenous non-starch polysaccharidases (a mixture of cellulase, xylanase, β-glucanase and mannanase) on the growth performance and nutrient digestibility, rumen fermentation, and rumen microflora of sheep. The animal trial was conducted using 36 5-month-old female fattening hybrid sheep (Duolang♂ × Hu♀) who were randomly assigned into four groups comprising nine sheep per treatment: CON, T1, T2, and T3, with 0, 0.1, 0.3, and 0.5% NSPases/kg DM of TMR, respectively. This complex enzyme product was screened for optimal ratios based on previous in vitro tests and responded positively to the in vitro fermentation of the TMR. When treated with NSPases, there was a non-linear effect of average daily gain and feed conversion rate, with the greatest improvement observed in the T2 group. There were no significant differences (p > 0.05) in nutrient intake or apparent digestibility among the NSPase-supplemented groups. In addition, T2 group had a significantly higher acetate to propionate ratio and pH (p < 0.05) than the other groups, and NH3-N and microbial protein concentrations showed a quadratic curve. The results revealed that both immunoglobulins and serum hormones increased linearly with addition (p < 0.05). As the T2 group showed the best growth performance, the CON and T2 groups were subjected to rumen metagenomic analysis. The results showed higher abundance of bacteria and lower abundance of Viruses in the rumen microbiota of the T2 group compared to the CON group. In addition, Uroviricota and Proteobacteria abundance was significantly lower in the T2 group than in the CON group at the phylum level (p < 0.05). These results suggest that the supplementation of high-concentrate rations with NSPases enhance immunity, reduces virus abundance in the rumen, improves rumen health, and promotes rumen fermentation. Our findings provide novel insights for improving growth performance and alleviating inflammatory responses arising from high concentrate feeding patterns in ruminants. However, the biological mechanisms cannot be elucidated by exploring the composition of rumen microbe alone, and further studies are required.

Evolutionary game analysis on collaborative logistics diffusion considering diminishing marginal utility under dynamic productivity

Reducing carbon emissions in the transportation sector is crucial for sustainable practices, with collaborative logistics diffusion playing a significant role in promoting energy-saving and emission-reduction strategies. This paper introduces an evolutionary game model to analyze collaboration between manufacturers and logistics service providers (LSPs), using the Hotelling quadratic curve model to measure the diminishing marginal utility of basic profits. Initially, a static strategy leads to a cyclic evolution without reaching the evolutionary stable strategy (ESS), reflecting competitive dynamics under static productivity conditions where neither party gains a lasting advantage, leading to periodic adjustments in strategies. The Cobb-Douglas function models a dynamic productivity strategy that regulates the extra benefits of collaborative logistics and penalties for 'free-riding.' This strategy demonstrates an inward spiral convergence towards the ESS, showing that adaptive mechanisms enable manufacturers and LSPs to align interests and achieve equilibrium. Enhanced benefits from collaborative logistics promote a stable and cooperative ecosystem, discouraging free-riding and enhancing cost efficiency. Moreover, increased investment by manufacturers not only strengthens their position but also fosters an environment conducive for LSP participation, expediting collaborative logistics diffusion and minimizing potential losses.

Morphology-based selective breeding strategy analysis for abdominal meat yield in Procambarus clarkii

The edible portion of Procambarus clarkii mainly consists of the abdominal muscles, highlighting the genetic enhancement of abdominal meat yield in breeding. To explore a selective breeding strategy for abdominal meat yield, the correlation of morphological characteristics with abdominal meat yield based on five P. clarkii populations collected from its major production areas in China was analyzed and an optimal prediction model was constructed for predicting abdominal meat yield. With the analyses of P. clarkii morphological characteristics, Fulton's condition factor (K), which had a strong negative correlation (-0.800 in males and - 0.705 in females) with abdominal meat yield and the advantage of not requiring the sacrifice of breeding candidates, was eventually selected as the morphological predictor. And the optimal prediction model constructed based on K value was a quadratic curve, with R2 values of 0.684 for males and 0.590 for females, and correlation coefficients of 0.827 and 0.768 between observed and predicted values for males and females, respectively. The results of the abdominal meat yield selective breeding experiment, utilizing the optimal prediction model, demonstrated that the breeding population exhibited favorable morphological variation as expected. These findings provide a morphology-based selection strategy for breeding the abdominal meat yield of P. clarkii.

Computing nodes for plane data points by constructing cubic polynomial with constraints

To construct a parametric polynomial curve for interpolating a set of data points, the interpolation accuracy and shape of the constructed curve are influenced by two principal factors: parameterization of the data points (computing a node for each data point) and interpolation method. A new method of computing nodes for a set of data points was proposed. In this paper, the functional relationship between data points and corresponding nodes in cubic polynomials was established. Using this functional relationship, a functional cubic polynomial with one degree of freedom can pass through four adjacent data points. The degree of the freedom can be represented by two adjacent node intervals can be obtained by minimizing the cubic terms of the cubic polynomial. Since each node is computed in different node spaces, a method for constructing a quadratic curve is presented, which transforms all the quadratic curves into a unified form to compute nodes. Nodes computed using the new method exhibit quadratic polynomial precision, i.e., if the set of data point is taken from a quadratic polynomial F(t), the nodes by the new method are used to construct a interpolation curve, an interpolation method reproducing quadratic polynomial gives quadratic polynomial F(t). The primary advantage of the proposed method is that the constructed curve has a shape described by data points. Another advantage of the new method is that the nodes computed by it have affine invariance. The experimental results indicate that the curve constructed by the nodes using the new method has a better interpolation accuracy and shape compared to that constructed using other methods.

Periapsis shift in spherically symmetric spacetimes and effects of electric interactions* *This work is partially Supported by the Wuhan University Research Development Fund

The periapsis shift of charged test particles in arbitrary static and spherically symmetric charged spacetimes are studied. Two perturbative methods, the near-circular approximation and post-Newtonian methods, are developed and shown to be very accurate when the results are determined to high orders. The near-circular approximation method is more precise when eccentricity e of the orbit is small, whereas the post-Newtonian method is more effective when orbit semilatus rectum p is large. Results from these two methods are shown to agree when both e is small and p is large. These results are then applied to the Reissner-Nordström spacetime, the Einstein-Maxwell-dilation gravity, and a charged wormhole spacetime. The effects of various parameters on the periapsis shift, particularly that of the electrostatic interaction, are carefully studied. The periapsis shift data of the solar-Mercury are then used to constrain the charges of the Sun and Mercury, and the data of the Sgr A*-S2 periapsis shift are used to determine, for the first time using this method, the constraints of the charges of Sgr A* and S2.

A modification to the Friedman and Ortega isoconversional methods for evaluation of the activation energy as a function of conversion and temperature

The Friedman and Ortega isoconversional methods typically apply linear regression to the isoconversional kinetic data for calculation of activation energy solely as a function of extent of conversion. However, in complex reactions, activation energy depends on both conversion and temperature. Our modification involves quadratic curve fitting instead of linear regression, resulting in the determination of activation energy as a function of conversion and temperature. The new technique enables the calculation of the temperature dependence of activation energy for different heating rates, making it a valuable addition to isoconversional analysis. The conventional and modified approaches were utilized on the isoconversional kinetic data concerning polyethylene thermal degradation. The results provided a more detailed representation of the variations in activation energy when nonlinear regression was used.

High dynamic range 3D shape reconstruction: Combination of adaptive fringe intensity, iterative exposure time adjustment and least quadratic curve fitting

For three-dimensional (3D) reconstruction of specular surfaces based on fringe projection profilometry (FPP), a hybrid approach combining adaptive fringe projection, iterative exposure time adjustment and least quadratic curve fitting is proposed. First, we propose an adaptive projection fringe intensity generation method in the camera image. Second, we build a new pixel matching between the camera and projector, and correct the pixel matching on the specular surfaces based on linear interpolation. Third, we propose an iterative exposure time adjustment method based on saturated pixel statistics. Fourth, we fuse the multiple results to obtain the final 3D reconstructed surface. Finally, we adopt a least quadratic curve fitting algorithm to fit the residual phase errors. Experiments confirmed the validity of the proposed method.

Taurine prevented the decline of fillet quality and muscle antioxidant capacity in on-growing grass carp (Ctenopharyngodon idella) fed non-fishmeal diet

Taurine is abundantly present in fishmeal, while plant protein sources typically contain minimal to no taurine. This disparity in taurine content may explain variations in fish quality traits caused by the dietary substitution of fishmeal with plant protein sources. This research explored whether taurine supplementation to non-fishmeal (NFM) diet could improve fillet quality and muscle antioxidant capacity in grass carp. A total of 540 fish (255.74 ± 0.65 g) were distributed among six groups. One of them was provided with a fishmeal (FM) diet, while the remaining five groups received NFM diets, formulated with incremental concentrations of crystalline taurine (0, 0.5, 1.0, 1.5, 2.0 g/kg) for 60 days. Our data showed that, in comparison with the un-supplemented group, the optimal taurine supplementation to NFM diet yielded the following findings: (1) increased fillet nutritional values by improving crude protein content, free amino acid and fatty acid compositions; (2) improved fillet physicochemical properties by improving water holding capacity (WHC), tenderness, and preventing pH decline; (3) enhanced antioxidant enzymes activities and gene expressions through nuclear factor-erythroid 2-related factor 2 (Nrf2) signaling pathway. Additionally, this optimal NFM diet showed to be competitive with FM diet in terms of fillet quality. According to quadratic regression curves of ROS production and polyunsaturated fatty acids (PUFA) content, the optimal taurine supplementation levels in NFM diet for on-growing grass carp were 1.12 and 1.18 g/kg diet, respectively.

Theory and inverse design of microperforated panels comprising arbitrary axial pore profiles for broadband low-frequency sound absorption

Toward identifying efficient sound absorbers, we have formulated and analyzed the micro-perforated panels (MPPs) comprising cylindrical pores of arbitrary axial profiles for out-of-plane wave propagation. First, the forward problem was solved wherein an exact analytical expression for the absorption coefficient α was developed for these MPPs. The dependence of α was analyzed for various profiles comprising convex and concave-shaped sections including divergent and convergent linear and sinusoidal profiles, conic sections, Kilroy, and chirp shapes. The MPPs with pores having a diverging shape at the entrance were found to have higher sound absorption. The non-symmetric fluctuations in the profile led to fluctuations in the spectrum of α. Aiming to address the long-standing challenge of low-frequency sound absorption, we solved the inverse problem to identify the axial profile of the cylindrical pore for maximum sound absorption for frequencies up to 2500 Hz. Given the advances in additive manufacturing, the results of this comprehensive work help in designing MPPs comprising complex-shaped pores suitable for a particular spectral regime.

Estimation of Quadratic Food Engel Curve in the presence of Measurement Error and Endogeneity of Total Expenditure in Pakistan

This study is conducted to compare the four different estimation techniques, Ordinary least square, Instrumental Variable, Lewbel (1996) approach and control function approach estimating the quadratic food Engel curve in the presence of the problem of measurement error and the problem of endogeneity of total expenditure. The authors have used the HIES data 2010-11 as it has been observed that the HIES data 2010-11 fits a quadratic shape of food Engel curve in Pakistani context. Moreover, the expenditure elasticity of food demand was observed between zero and one which indicates the fact that food is a necessary good for Pakistani households. The results also shows that endogeneity of total expenditure is more serious issue than the measurement error.

On Conic Equations Under Bernstein Operators

One of the most important problems in approximation theory in mathematical analysis is the determination of sequences of polynomials that converge to functions and have the same geometric properties. This type of approximation is called the shape-preserving approximation. These types of problems are usually handled depending on the convexity of the functions, the degree of smoothness depending on the order of differentiability, or whether it satisfies a functional equation. The problem addressed in this paper belongs to the third class. A quadratic bivariate algebraic equation denotes geometrically some well-known shapes such as circles, ellipses, hyperbolas and parabolas. Such equations are known as conic equations. In this study, it is investigated whether conic equations transform into a conic equation under bivariate Bernstein polynomials, and if so, which conic equation it transforms into.

Hand-eye calibration of line structured-light sensor by scanning and reconstruction of a free-placed standard cylindrical target

This paper proposed a hand-eye calibration method for a line structured-light (LSL) scanner mounted on industrial robot. Unlike widely used spherical targets, the target used in our work is a cylinder, which is inexpensive and easy to be manufactured in larger size to cover a wider calibration space. In order to address the profile self-occlusion and drastically shape changing of conic section during calibration, an unconstrained dimensionality reduction method is proposed to fit the scanned profiles. Based on fitted ellipse centers under various robot poses, the hand-eye calibration model is developed based on the difference between cylinder radius and the distance from the profile point to the cylinder axis. Simulation and actual experiments have shown that the proposed ellipse fitting method is more accurate and robust, and the calibration method achieves higher reconstruction accuracy under the same robot positioning error, need less robot operations to obtain more accurate hand-eye parameters.

Patterns and predictors of alcohol misuse trajectories from adolescence through early midlife.

We took a multilevel developmental contextual approach and characterized trajectories of alcohol misuse from adolescence through early midlife, examined genetic and environmental contributions to individual differences in those trajectories, and identified adolescent and young adult factors associated with change in alcohol misuse. Data were from two longitudinal population-based studies. FinnTwin16 is a study of Finnish twins assessed at 16, 17, 18, 25, and 35 years (N = 5659; 52% female; 32% monozygotic). The National Longitudinal Study of Adolescent to Adult Health (Add Health) is a study of adolescents from the United States, who were assessed at five time points from 1994 to 2018 (N = 18026; 50% female; 64% White, 21% Black, 4% Native American, 7% Asian, 9% Other race/ethnicity). Alcohol misuse was measured as frequency of intoxication in FinnTwin16 and frequency of binge drinking in Add Health. In both samples, trajectories of alcohol misuse were best described by a quadratic growth curve: Alcohol misuse increased across adolescence, peaked in young adulthood, and declined into early midlife. Individual differences in these trajectories were primarily explained by environmental factors. Several adolescent and young adult correlates were related to the course of alcohol misuse, including other substance use, physical and mental health, and parenthood.

Construction of exact and asymptotic solutions for the problem of torsional vibrations of a radially inhomogeneous sphere

In this paper, the torsional vibrations of a radially inhomogeneous isotropic open sphere containing no 0 and π poles are studied. It is considered that the elastic moduli and density of the material are linear functions of the radius of the sphere. Cases are considered when the lateral surface of the sphere is stress-free and fixed, and arbitrary boundary conditions are specified on conic sections. The formulated boundary value problems are reduced to spectral problems. After fulfilling boundary conditions specified on the lateral surfaces of the sphere, a dispersion equation is obtained. Exact solutions to the problem are constructed. Next, we analyzed the roots of the dispersion equation for a relatively small parameter characterizing the thickness of the sphere, depending on the oscillation frequency. For a sphere of small thickness, asymptotic zeros are constructed, and their characteristics are studied.

Does Gender Kuznets Curve Exist in South Asian Countries? Role of Gender Equality and Economic Development

This study aims to determine the relationship between gender equality and economic growth in major South Asian countries. This study suggests checking the gender Kuznets curve or whether the data support a linear, quadratic, or cubic gender Kuznets curve for major South Asian countries. We used time series data and covered the period from 1980 to 2019. We applied the Ng-Perron unit root test to check for non-stationary time series data. After the integration order is established, the autoregressive distributive lag (ARDL) model is used in three steps. The ARDL bound testing approach of covariance shows that Sri Lanka has an S-shaped Gender Cognition Curve (GKC), India has a Z-shaped GKC, Pakistan has an S-shape, and Bangladesh has an S-shape. is the -shaped GKC association. Periods of countries were considered. We also conclude that gender equality is not a direct result of development. Consequently, politicians with gender equality policies should subsidize women's employment in times of financial hardship.

A more accurate piecewise linear approximation method for quadratic cost curves of thermal generators and its application in unit commitment

A more accurate piecewise linear approximation method for quadratic cost curves of thermal generators and its application in unit commitment