Quartic Model Research Articles

Constructive expansion for vector field theories I. Quartic models in low dimensions

This paper is the first of a series aiming to use the loop vertex expansion (LVE) to recover or prove analyticity and Borel summability for generic vector models with bosonic or fermionic statistics in various dimensions. We consider both non-relativistic and relativistic bosons and fermions coupled with a constant quartic tensor in zero-, one-, and two-dimensional space by limiting our investigations to the super-renormalizable models. This offers a unified perspective on classical constructive results, highlighting the usefulness of the LVE as a modern tool to address these questions and to tackle more challenging models in higher dimensions. Finally, we investigate the large N and massless limits along with quenching for fermions in one dimension. In particular, this work establishes the Borel summability of the Sachdev–Ye–Kitaev model.

Polynomial modeling of emergency department arrivals: An analysis of local and national utilization patterns

Emergency department (ED) overcrowding is a national problem that is associated with ambulance diversion, decreased patient and provider satisfaction and poor patient outcomes. This study presents a novel approach to modeling the relationship between time of day, day of week, and ED arrivals using a hierarchical polynomial regression model. A series of hierarchical regression models were created to determine polynomial effects and capture the covariability (defined as R2) of the relationships from the 2009 to 2017 National Hospital Ambulatory Medical Care Survey (NHAMCS) Emergency Department Public Use Data File and institutional data from a regional medical center from 2018 to 2019. The following hierarchical regression models were constructed: cubic main effects, cubic interaction effects, quartic main effects, quartic interaction effects, quintic main effects, and quintic interaction effects. Based on maximal improvement in R2 and significance of each of the four effects in both the national and institutional data sets, the quartic main effects model was determined to be optimal for describing ED arrival patterns. In alignment with prior studies, significantly higher ED arrival volumes were observed on Mondays in comparison to all other weekdays.

Corrosion mitigation performance of disodium EDTA functionalized chitosan biomacromolecule - Experimental and theoretical approach

Disodium ethylenediaminetetraacetate salt is known for its excellent coordinating properties with the metal ions. The present study deals with the investigation of the prepared Disodium EDTA functionalized chitosan in corrosion inhibition for mild steel in 1 M HCl. The modified chitosan was characterized by spectral studies, thermal analysis, and Zeta potential studies. The corrosion inhibition efficiency (%) was evaluated using the gravimetric method and electrochemical studies. The electrochemical studies included potentiodynamic polarization, linear polarization resistance, and electrochemical impedance methods. The modified chitosan polymer showed an inhibition efficiency of 96.63% for 500 ppm at 303 K. Adsorption process obeyed Langmuir isotherm. Experimental results and theoretical calculations endorsed initial physisorption followed by a chemisorption process. Surface characterization studies supported the formation of a protective film that enabled the inhibition process. Density functional theory, Monte Carlo studies, and molecular dynamics simulation studies show a good agreement with the experimental results. Two-way Analysis of Variance was performed to test the influence of immersion period and inhibitor concentration on the corrosion rate using the statistical software IBM SPSS 20.0. A quartic model was generated as the best fit with the highest R2 value of 0.973. Design Expert software was employed for statistical modeling fit.

Optimization of Congo red dye adsorption from wastewater by a modified commercial zeolite catalyst using response surface modeling approach.

In the present work, Zeolite A was modified by using hexadecyltrimethylammonium bromide (HDTMABr) for adsorption of the Congo red (CR) dye from synthetic aqueous solutions. The Modified Zeolite A (MZA) was characterized by XRD, SEM, and FTIR. The influence of solution pH (in the 4-12 range), ionic strength (0.1-1 M), contact time (180 min), initial CR concentration (20-60 mg/L), temperature (24-36 °C), and an adsorbent dose (1-3 g m/L) on the % dye removal and adsorbent capacity were studied. A combined effect of the initial CR concentration and temperature on the CR removal % by MZA was also studied by applying response surface methodology (RSM). Experimental values were in a good agreement with those predicated by a second-order quartic model. A maximum of 99.24% dye removal and adsorbent capacity of 21.11 mg/g was achieved under the following conditions: pH = 7, initial CR concentration = 60 mg/L, temperature = 24 °C, ionic strength = 0.1 M, adsorbent dose = 3 g/L and 90 min contact time. The equilibrium data were subjected to the Langmuir, Freundlich and Temkin isotherms, with the latter providing the best fit while kinetic adsorption studies were conducted by applying three models. The results indicated that the removal process was best described by the pseudo-second-order model. The present study demonstrates that modified MZA can be utilized for the highly efficient CR dye removal.

Review on Aluminum and Steel Semi-rigid Connections Behavior Design Model

Several research reports agree on the influence of joint rotational behavior on the stability of space frames. One must therefore consider it in space structures study. Joint rotational behavior is generally considered in space structures study by means of its moment-rotation behavior curve. Models such as analytical, empirical, experimental, informational, mechanical and numerical mostly are used to determine joint mechanical behavior. This review paper presents an overview of available methods for the prediction of semi rigid connections behavior of under both static and dynamic loads. Advantages, disadvantages, and principal characteristics of each model stretched out. The modeling of joint behavior in studying space structures is associated with a mathematical representation model of the joint moment-rotation curve. Several models, linear, bilinear, multilinear and nonlinear representations are developed through the years to picture accurately the joints moment rotation behavior. The most precise representation applies continuous nonlinear functions, even though the multilinear representation is generally used for mechanical models. Using test data on aluminum and steel bolted connections conducted at Harbin Institute of Technology a simple stable quartic polynomial model is proposed to represent the behavior of the connections. In addition, Three others models are also proposed, including an Odd power Polynomial Model as proposed by Frye & Morris Model, a three parameter Power Model in accordance to the Kishi & Chen Model, and a four-parameter exponential model in line with the Yee & Melchers Model. These three models are compared with the simple quartic polynomial model proposed in this paper. As a result, the proposed connection design model, independent of test data, can be used directly by designers to assess semi-rigid, bolted connection behavior in Space Structures. The present work will give support to engineers for easy and accurate choice of the joint behavior prediction model and portrait correctly the behavior of the joints for best use in semi-rigid space structures construction.

A kernel-free double well potential support vector machine with applications

As a well-known machine learning technique, support vector machine (SVM) with a kernel function achieves much success in nonlinear binary classification tasks. Recently, some quadratic surface SVM models are proposed and studied by utilizing quadratic surfaces for nonlinear binary separations. In this paper, a kernel-free soft quartic surface SVM model is proposed by utilizing the double well potential function for highly nonlinear binary classification. Mathematical analysis on the theoretical properties of the proposed model, including the existence, uniqueness and support vector representation of optimal solutions, is shown. The sequential minimal optimization algorithm is adopted to implement the proposed model for computational efficiency. Numerical results on some artificial and public benchmark data sets demonstrate its effectiveness over well-known SVM models with or without kernel functions. The proposed model is extended to successfully handle some real-life corporate and personal credit data sets for applications.

Quartic Horndeski, planar black holes, holographic aspects and universal bounds

In this work, we consider a specific shift-invariant quartic Horndeski model, deriving new planar black hole solutions with axionic hair. We explore these solutions in terms of their horizon structure and their thermodynamic properties. We use the gauge/gravity dictionary to derive the DC transport coefficients of the holographic dual with the aim of investigating how the new deformation affects the universality of some renown bound proposals. Although most of them are found to hold true, we nevertheless find a highly interesting parametric violation of the heat conductivity-to-temperature lower bound which acquires a dependence on both the scale and the coupling. Finally, using a perturbative approach, a more brutal violation of the viscocity-to-entropy ratio is demonstrated.

Simulation and optimisation of the pyrolysis of rice husk: Preliminary assessment for gasification applications

Thermochemical conversion of biomass into useful products is a promising route to harness biofuels. This process is clean, renewable and can reduce the use of fossil fuel. In this study, SuperPro Designer (SPD) software and response surface methodology (RSM) is used to simulate and optimize rice husk pyrolysis process. The SPD simulator was built to handle kinetics and stoichiometric reaction of lignocellulosic composition of rice husk into final products. The SPD simulation and RSM optimization were performed at a temperature ranging from 350 to 800 °C and residence time of 0.25−60 s. The simulated results were in agreement with product yield published in the literature at an average relative error of 6.8 %. The combined effect of temperature and residence time were analysed by using RSM and analysis of variance (ANOVA). A cubic model for bio-oil and quartic model for char and gas yield were proposed. The desirability function in Design-Expert showed that the optimum bio-oil yield (36.72 %) could be attained at a temperature 588 °C and a residence time 0.25 s while the optimum gas yield (73.25 %) could be achieved at a temperature 798.8 °C and a residence time 15.47 s. These findings therefore revealed that the energy content of the rice husk could be harnessed by pyrolysis/gasification to obtain substantial fuel products.

Performance improvement of empirical models for estimation of global solar radiation in India: A k-fold cross-validation approach

In this work, global solar radiation is estimated based on sunshine duration. Solar radiation measurements have been collected from the Indian Meteorological Department (Pune, India) for the period 1986–2000. 25 model forms were selected from the literature which correlates the clearness index with sunshine duration. The coefficients of models are extracted from the data. k-fold cross-validation is then employed to improve the performance of the models. Data is split into k-groups with each group containing the same amount of data. (k-1) groups are utilized for the development of models and the rest one group is utilized for the testing of models performance. The procedure is repeated k-times and those coefficients are selected which produces the least error. Models are evaluated and compared with the help of statistical errors. Further, the statistical errors were scaled and Global Performance Indicator (GPI) was evaluated. Using GPI, models were given rank in order of suitability of estimates produced. The GPI value lies between −9.4269 and 0.4695. It has been observed that the quartic model (M-04) exhibited the best performance with MBE = 0.0259, RMSE = 1.7927, MPE = 0.1495, RRMSE = 0.0352, erMAX = 0.9072, MARE = 0.0812, MAE = 1.3843, U95 = 6.3100, t-stats = 0.2397 and R = 0.8597 resulting in the highest GPI amongst all the models which were proposed.

Modeling Nigerian Covid-19 cases: A comparative analysis of models and estimators.

COVID-19 remains a major pandemic currently threatening all the countries of the world. In Nigeria, there were 1, 932 COVID-19 confirmed cases, 319 discharged cases and 58 deaths as of 30th April 2020. This paper, therefore, subjected the daily cumulative reported COVID-19 cases of these three variables to nine (9) curve estimation statistical models in simple, quadratic, cubic, and quartic forms. It further identified the best of the thirty-six (36) models and used the same for prediction and forecasting purposes. The data collected by the Nigeria Centre for Disease Control for sixty-four (64) days, two (2) months and three (3), were daily monitored and eventually analyzed. We identified the best models to be Quartic Linear Regression Model with an autocorrelated error of order 1 (AR(1)); and found the Ordinary Least Squares, Cochrane Orcutt, Hildreth-Lu, and Prais-Winsten and Least Absolute Deviation (LAD) estimators useful to estimate the models' parameters. Consequently, we recommended the daily cumulative forecast values of the LAD estimator for May and June 2020 with a 99% confidence level. The forecast values are alarming, and so, the Nigerian Government needs to hastily review her activities and interventions towards COVID-19 to provide some tactical and robust structures and measures to avert these challenges.

Inflation models in the light of self-interacting sterile neutrinos

Short baseline neutrino experiments, like LSND and MiniBooNE experiments, pointed towards the existence of eV mass scale sterile neutrinos. To reconcile sterile neutrinos with cosmology self interaction between sterile neutrinos has been studied. We analysed Planck cosmic microwave background (CMB) data with self-interacting sterile neutrino (SI$\nu$) and study their impact on inflation models. The fit to the CMB data in SI$\nu$ model is as good as the fit to $\Lambda$CDM model. We find that the spectral index ($n_s$) values shift to $0.9361\pm 0.0055$ in SI$\nu$ model. This has significant impact on the validity of different inflation models. For example the Starobinsky and quartic hilltop model, which were allowed within $\Lambda$CDM cosmology, are ruled out. On the other hand some models like natural and Coleman-Weinberg inflation are now favoured. Therefore, the existence of self interacting sterile neutrinos with eV order of mass will play an important role in the selection of correct inflation model.

Simultaneous Optimization of Biomass and Metabolite Production by a Microalgae-Yeast Co-culture Under Inorganic Micronutrients

Enhancing the productivity of biomass, carbohydrates, proteins, and lipids in microalgae cultures is an essential task to justify the feasibility of using biofuels as energetic alternatives to fossil fuels. Diverse strategies can be used to get a biologically plausible optimization of the microalgae culture such as using indigenous microalgae added with other microorganisms such as fungi or bacteria, analyzing the effect of culture broth composition and reaction experimental conditions. A wastewater isolated co-culture microalgae-yeast (CCMY) was evaluated as potential biomass and lipids-efficient producer. The Box-Behnken experimental design and the response surface methodology yield to identify the best attainable composition of inorganic nutrient variables in culture media: sodium nitrate (NaNO3), potassium phosphate (K2HPO4), and ferrous sulfate (FeSO4). The results of the experimental design revealed that the NaNO3, K2HPO4, and FeSO4 were three factors significantly influencing the biochemical content. The detected optimal conditions correspond to a highest biomass production of 1.68 g L−1; the carbohydrate content was 16.75%, for proteins 37.11%, and the maximum lipid content was 27.77%. These values were about two times higher than the results obtained with the original version of the culture broth (BBM). The complexity of inorganic salts effect on the biomass and lipid accumulation motivates the proposal of a quartic order mathematical model which characterizes the productivity of microalgae-yeast co-culture as function of the inorganic micronutrient contents.

Generators and integral points on elliptic curves associated with simplest quartic fields

Abstract We associate to some simplest quartic fields a family of elliptic curves that has rank at least three over ℚ(m). It is given by the equation E m : y 2 = x 3 − 36 36 m 4 + 48 m 2 + 25 36 m 4 − 48 m 2 + 25 x . $$\begin{array}{} \displaystyle E_m:y^2=x^3-36\left(36m^4+48m^2+25\right)\left(36m^4-48m^2+25\right)x. \end{array}$$ Employing canonical heights we show the rank is in fact at least three for all m. Moreover, we get a parametrized infinite family of rank at least four. Further, the integral points on the curve Em are discussed and we determine all the integral points on the original quartic model when the rank is three. Previous work in this setting studied the elliptic curves associated with simplest quartic fields of ranks at most two along with their integral points (see [2, 3]).

Modelling and Optimization of the Wear rate, Compressive Strength and Hardness of a Composite Brake Pad

A composite brake pad of periwinkle shell, phenolic resin and other additives was developed. The mixture design experiment was adopted using the Design Expert 10.0 software 2017 version and the sample composites were produced using compression molding. Mathematical models of the wear rate, compressive strength and hardness values were developed and validated. The models for the wear rate and compressive strength fitted best with the quartic response model while that of the hardness suited best with quartic and linear models. Comparison of the models with experimental results graphically showed high degree of correlation. An optimized formulation with an objective of minimization of the wear rate and maximization compressive strength and hardness value was determined at 50, 30 and 20% of periwinkle shell powder (filler), phenolic resin (matrix) and additives respectively. Thus the mathematical model can be used to predict the wear rate, compressive strength and hardness value of the experimental design adopted.Key words: periwinkle shell; composite brake pad; quartic mathematical model; wear rate; compressive strength; hardness value; mixture design

Isogeny formulas for Jacobi intersection and twisted hessian curves

The security of public-key systems is based on the difficulty of solving certain mathematical problems. With the possible emergence of large-scale quantum computers several of these problems, such as factoring and computing discrete logarithms, would be efficiently solved. Research on quantum-resistant public-key cryptography, also called post-quantum cryptography (PQC), has been productive in recent years. Public-key cryptosystems based on the problem of computing isogenies between supersingular elliptic curves appear to be good candidates for the next generation of public-key cryptography standards in the PQC scenario. In this work, motivated by a previous work by D. Moody and D. Shumow [17], we derived maps for elliptic curves represented in Jacobi Intersection and Twisted Hessian models. Our derivation follows a multiplicative strategy that contrasts with the additive idea presented in the Vélu formula. Finally, we present a comparison of computational cost to generate maps for isogenies of degree $ l $, where $ l = 2k + 1 $. In affine coordinates, our formulas require $ 46.8 \% $ less computation than the Huff model and $ 48\% $ less computation than the formulas given for the Extended Jacobi Quartic model when computing isogenies of degree $ 3 $. Considering higher degree isogenies as $ 101 $, our formulas require $ 23.4\% $ less computation than the Huff model and $ 24.7 \% $ less computation than the formula for the Extended Jacobi Quartic model.

Generalized Galileon scenario inspires chaotic inflation

We study chaotic inflation with a Galileon-like self-interaction G(phi ,X)Box phi , where G(phi ,X)propto X^{n}. General conditions required for successful inflation are deduced and discussed from the background and cosmological perturbations under slow-roll approximation. Interestingly, it is found that in the regime where the Galileon term dominates over the standard kinetic term, the tensor-to-scalar ratio becomes significantly suppressed in comparison to the standard expression in General Relativity (GR). Particularly, we find the allowed range in the space of parameters characterizing the chaotic quadratic and quartic inflation models by considering the current observational data of Planck from the n_{mathcal {S}}-r plane. Finally, we discuss about the issue if the Galileon term is dominant by the end of inflation, this can affect the field oscillation during reheating.

Modeling Changes in Corneal Parameters With Age: Implications for Corneal Disease Detection

To apply computational methods to model normal age-related changes in corneal parameters and to establish their association with demographic factors, thereby providing a framework for improved detection of subclinical corneal ectasia (SCE). Cross-sectional study. One hundred seventeen healthy participants were enrolled from Centre for Eye Health (Sydney, Australia). Corneal thickness (CT), front surface sagittal curvature (FSSC), and back surface sagittal curvature (BSSC) measurements were extracted from 57 corneal locations from 1 eye per participant using the Pentacam HR. Cluster analyses were performed to identify locations demonstrating similar variations with age. Age-related changes were modeled using polynomial regression with sliding window methods, and model accuracy was verified with Bland-Altman comparisons. Pearson correlations were applied to examine the impacts of demographic factors. Concentric cluster patterns were observed for CT and FSSC but not for BSSC. Sliding window analyses were best fit with quartic and cubic regression models for CT and FSSC/BSSC, respectively. CT and FSSC sliding window models had narrower 95% limits of agreement compared with decade-based models (0.015mm vs 0.017mm and 0.14mm vs 0.27mm, respectively), but were wider for BSSC than decade-based models (0.73mm vs 0.54mm). Significant correlations were observed between CT and astigmatism (P=.02-.049) and FSSC and BSSC and gender (P=<.001-.049). The developed models robustly described aging variations in CT and FSSC; however, other mechanisms appear to contribute to variations in BSSC. These findings and the identified correlations provide a framework that can be applied to future model development and establishment of normal databases to facilitate SCE detection.

Simplified model for estimations of combustion products, adiabatic flame temperature and properties of burned gas

To reduce complications in calculations of mole fractions of combustion products, adiabatic flame temperature and burned gas properties, a simplified calculation of combustion products is proposed in this work. 6 major gas species are considered in burned gas. 6 governing equations are reduced to a fourth degree polynomial equation and it is referred to as quartic combustion model (QCM). The calculations of adiabatic flame temperature, thermodynamic properties and transport properties of burned gas are also presented. The combustions of fuels are simulated using the developed model and the results are compared with those using Chemical Equilibrium and Applications program (CEA) in which 10 gas species are accounted. The comparison results show that, for non-preheated reactant mixture, the mole fractions of major species of combustion products, the adiabatic flame temperature and the thermodynamic properties from QCM are slightly different from that of CEA. Furthermore, the QCM estimates the numbers of moles of the combustion products more precise than that from low temperature combustion model. However, the viscosity and the thermal conductivity calculated using QCM are possibly 4.5% and 5.4% lower than that obtained from CEA, respectively. For the Prandtl number, the QCM gives this property averagely 1% higher than that from CEA.

Boundary effects of expectation in human pain perception

Perception of sensory stimulation is influenced by numerous psychological variables. One example is placebo analgesia, where expecting low pain causes a painful stimulus to feel less painful. Yet, because pain evolved to signal threats to survival, it should be maladaptive for highly-erroneous expectations to yield unrealistic pain experiences. Therefore, we hypothesised that a cue followed by a highly discrepant stimulus intensity, which generates a large prediction error, will have a weaker influence on the perception of that stimulus. To test this hypothesis we collected two independent pain-cueing datasets. The second dataset and the analysis plan were preregistered (https://osf.io/5r6z7/). Regression modelling revealed that reported pain intensities were best explained by a quartic polynomial model of the prediction error. The results indicated that the influence of cues on perceived pain decreased when stimulus intensity was very different from expectations, suggesting that prediction error size has an immediate functional role in pain perception.

Modeling the remote-sensing reflectance of highly turbid waters.

In ocean-color remote sensing, subsurface remote-sensing reflectance (r r s ) of optically deep waters can be linked to its absorption (a) and backscattering coefficients (b b ) by various models. The use of such models allows for quick calculations r r s from such coefficients, eliminating the need to solve the radiative transfer equation. In particular, r r s can be expressed as a function of bb/(a+bb). HydroLight and Monte Carlo simulations showed that commonly used models underestimate r r s in waters with high suspended sediment loads. Monte Carlo simulations confirmed that this issue is due to a sharp increase in multiple scattering events at high turbidity levels. A quartic polynomial model is derived relating r r s and inherent optical properties (IOPs) for waters of any turbidity, to avoid significant errors in waters of high turbidity.