Constant Elasticity Research Articles

Adhesive peptide and polymer density modulate 3D cell traction forces within synthetic hydrogels

Cell-extracellular matrix forces provide pivotal signals regulating diverse physiological and pathological processes. Although mechanobiology has been widely studied in two-dimensional configurations, limited research has been conducted in three-dimensional (3D) systems due to the complex nature of mechanics and cellular behaviors. In this study, we established a platform integrating a well-defined synthetic hydrogel system (PEG-4MAL) with 3D traction force microscopy (TFM) methodologies to evaluate deformation and force responses within synthetic microenvironments, providing insights that are not tractable using biological matrices because of the interdependence of biochemical and biophysical properties and complex mechanics. We dissected the contributions of adhesive peptide density and polymer density, which determines hydrogel stiffness, to 3D force generation for fibroblasts. A critical threshold of adhesive peptide density at a constant matrix elasticity is required for cells to generate 3D forces. Furthermore, matrix displacements and strains decreased with matrix stiffness whereas stresses, and tractions increased with matrix stiffness until reaching constant values at higher stiffness values. Finally, Rho-kinase-dependent contractility and vinculin expression are required to generate significant 3D forces in both collagen and synthetic hydrogels. This research establishes a tunable platform for the study of mechanobiology and provides new insights into how cells sense and transmit forces in 3D.

Optimal Investment Strategy for DC Pension Plan with Deposit Loan Spread under the CEV Model

This paper is devoted to determining an optimal investment strategy for a defined-contribution (DC) pension plan with deposit loan spread under the constant elasticity of variance (CEV) model. As far as we know, few studies in the literature have taken loans into account when using the CEV model in financial market contexts. The contribution of this paper is to study the impact of deposit loan spread on DC pension investment strategy. By considering a risk-free asset, a risky asset driven by CEV model, and a loan in the financial market, we first set up the dynamic equation and the asset market model, which are instrumental in achieving the expected utility of ultimate wealth at retirement. Second, the corresponding Hamilton–Jacobi–Bellman (HJB) equation is derived by means of the dynamic programming principle. The explicit expression for the optimal investment strategy is obtained using the Legendre transform method. Finally, different parameters are selected to simulate the explicit solution, and the financial interpretation of the optimal investment strategy is provided. We find that the deposit loan spread has a great impact on the investment strategy of DC pension plans.

Borda-optimal taxation of labour income

I numerically compute Borda-optimal, i.e., optimal based on the Borda count as the normative criterion, labour-income tax schedules for the United States. I do so in the context of a Mirrlees-style model with quasilinear preferences and a constant elasticity of labour supply. Because the Borda count is defined for finitely many alternatives, the computations restrict attention to a finite subset of the set of continuous, piecewise linear tax schedules with (in the baseline analysis) four or fewer pieces.

The supply-side effects of cannabis legalization

ObjectiveThe purpose of this study is to examine how cannabis legalization and corresponding taxation would affect the supply-side of the cannabis market. Specifically, the study considers various scenarios in which Oklahoma legalizes recreational cannabis for adult use and simulates changes in state-level market sales for other legal states and the average grower profits in Oklahoma. We assume that legalizing recreational cannabis in medical-only states would significantly increase the demand quantity in the legalized states and the local government would levy a significant level of tax on recreational cannabis. These assumptions are based on the post-legalization phenomena in other legalized US states.MethodWe simulate outcomes in the cannabis industry under the assumption of representative consumers with constant elasticity of substitution demand behavior and profit-maximizing firms with a Cobb-Douglas profit function. All agents are assumed to take exogenous prices as given. We calibrate the model using state-level sales data from 2020 and explore potential policies in Oklahoma and at the federal level.ResultsWe find that, under the scenarios we consider, legalization of recreational cannabis in Oklahoma would lead to a decrease in the quantity of cannabis sold in Oklahoma’s medical cannabis market as well as decreases in the quantity of cannabis sold in other states on average. Furthermore, we find that as the excise tax rate on recreational cannabis in Oklahoma is increased, the demand quantity in recreational cannabis market would decrease while the other markets’ demand quantity would increase on average. As the elasticity of substitution between state-level products increases, the overall demand quantity would increase and the market quantity across states become more sensitive to Oklahoma’s tax policies. This pattern could become starker as the elasticity of substitution between recreational and medical cannabis increases. In terms of profit, heavy taxation and price decrease due to legalization would significantly decrease cannabis producers’ production and profit levels unless the cost reduction strategies complement legalization.ConclusionBased on our results, the legalization of recreational cannabis has the potential to generate tax revenue to fund critical government projects and services. However, such legalization would have to be done carefully because heavy excise taxes would decrease the legal cannabis market demand and growers’ profit, which would incentivize producers and consumers to move to the illicit cannabis market. Policymakers would have to compromise between the levels of interstate transportation and taxation to ensure that cannabis suppliers also realize some profit within the cannabis supply chain.

Revisiting taste change in cost-of-living measurement

This paper compares conditional and unconditional cost-of-living indexes (COLI) when tastes change, focusing on the Constant Elasticity of Substitution model. A consumer price index typically targets a conditional COLI, which evaluates price change given set of preferences. An unconditional COLI aims to also capture the welfare effects of changing tastes, but it requires stronger assumptions. Using retail scanner data for food and beverage products, I find COLIs conditioning on current period tastes exceed those conditioning on prior period tastes. Consistent with previous studies, I find an unconditional COLI tends to reflect negative direct contributions from taste change.

Modelo con elasticidad constante de la varianza: Una aplicación en la Bolsa de Valores de Lima

The objective of this article is to present the constant elasticity of variance model, its main probabilistic aspects, and we implement the stochastic Runge Kutta method to simulate the sample trajectories based on the data of the CREDITC1 asset of the Bank of Credit from Perú taken from the Lima stock exchange.

Simple Closed-Form Formulas for Conditional Moments of Inhomogeneous Nonlinear Drift Constant Elasticity of Variance Process

The stochastic differential equation (SDE) has been used to model various phenomena and investigate their properties. Conditional moments of stochastic processes can be used to price financial derivatives whose payoffs depend on conditional moments of underlying assets. In general, the transition probability density function (PDF) of a stochastic process is often unavailable in closed form. Thus, the conditional moments, which can be directly computed by applying the transition PDFs, may be unavailable in closed form. In this work, we studied an inhomogeneous nonlinear drift constant elasticity of variance (IND-CEV) process, which is a class of diffusions that have time-dependent parameter functions; therefore, their sample paths are asymmetric. The closed-form formulas for conditional moments of the IND-CEV process were derived without having a condition on eigenfunctions or the transition PDF. The analytical results were examined through Monte Carlo simulations.

What is the value of swappable batteries for a shared e-scooter service?

Swappable batteries have been deployed in several services of dockless shared e-scooters. This article provides an economic theory of swappable batteries in the production of a shared e-scooter service (S3). Explicitly modelled are the operations of battery swapping by “juicing tours”, as well as the wearing law of the electric batteries depending on the depth of discharge (DoD) that triggers the next swap. In the production model, the daily number of refills and the per-refill swapping cost are key variables as they link the field implementation and the swapping logistics functions to the other production functions of battery inventory, scooter inventory, energy charging, fleet maintenance and commercial. Thus the overall “refill strategy” interplays with the respective inventory policies of batteries and of scooters. The mathematical optimization of the production cost function is addressed in four stages, by optimizing in turn (i) the swapping tours, (ii) the target DoD, (iii) the battery energy capacity (BEC), (iv) the scooter body in terms of lifespan and energy consumption rate. Characteristic equations are established for the optimal per-refill cost, DoD, BEC, scooter lifespan and energy consumption rate. Two sets of specifications, namely Constant Elasticity and Affine Linear, are specified for the battery wearing law, the battery price and the scooter price: under either set the model admits an analytical solution. In a numerical study, it is shown that the S3 cost per unit of fed-in energy is one order of magnitude greater than the out-of-the-grid electricity price.

DeepPricing: pricing convertible bonds based on financial time-series generative adversarial networks

Convertible bonds are an important segment of the corporate bond market, however, as hybrid instruments, convertible bonds are difficult to value because they depend on variables related to the underlying stock, the fixed-income part, and the interaction between these components. Besides, embedded options, such as conversion, call, and put provisions are often restricted to certain periods, may vary over time, and are subject to additional path-dependent features of the state variables. Moreover, the most challenging problem in convertible bond valuation is the underlying stock return process modeling as it retains various complex statistical properties. In this paper, we propose DeepPricing, a novel data-driven convertible bonds pricing model, which is inspired by the recent success of generative adversarial networks (GAN), to address the above challenges. The method introduces a new financial time-series generative adversarial networks (FinGAN), which is able to reproduce risk-neutral stock return process that retains the unique statistical properties such as the fat-tailed distributions, the long-range dependence, and the asymmetry structure etc., and then transit to its risk-neutral distribution. Thus it is more flexible and accurate to capture the dynamics of the underlying stock return process and keep the rich set of real-world convertible bond specifications compared with previous model-driven models. The experiments on the Chinese convertible bond market demonstrate the effectiveness of DeepPricing model. Compared with the convertible bond market prices, our model has a better convertible bonds pricing performance than both model-driven models, i.e. Black-Scholes, the constant elasticity of variance, GARCH, and the state-of-the-art GAN-based models, i.e. FinGAN-MLP, FinGAN-LSTM. Moreover, our model has a better fitting capacity for higher-volatility convertible bonds and the overall convertible bond market implied volatility smirk, especially for equity-liked convertible bonds, convertible bonds trading in the bull market, and out-of-the-money convertible bonds. Furthermore, the Long-Short and Long-Only investment strategies based on our model earn a significant annualized return with 41.16% and 31.06%, respectively, for the equally-weighted portfolio during the sample period.

Energy efficiency and energy rebound, intensity, and output effects in transport sector of Pakistan.

According to Jevon's paradox, energy efficiency leads to more energy consumption instead of low. So, calculating the size of energy rebound effect is need of the time to devise sustainable environmental and energy policies. This paper aims to analyze the impact of energy efficiency on energy consumption of transport sector in Pakistan by using time series data from 1980 to 2018. This incremental energy consumption channelizes through intensity and output effects. The study uses both Cobb-Douglas (C-D) and constant elasticity of substitution (CES) aggregate production functions to find the magnitudes of energy rebound effect. As the analysis of energy rebound effect is sensitive to the selection of data, model, and methodology. C-D production function deals with energy rebound effect, while CES provides extra information in the form of energy intensity and output effects along with energy rebound effect. The C-D function is estimated with linear estimation technique, while the CES function is estimated through nonlinear optimization method. The results indicate relatively low magnitudes of energy rebound effect in case of C-D function, e.g., 2% in the short run and about 36% in the long run while about 70% energy rebound, 63% energy intensity, and 7% output effect in the transport sector of Pakistan in the long run by using CES function. As anticipated, energy efficiency is less effective in terms of energy savings in transport sector due to energy rebound effect. Therefore, policy makers should incorporate energy rebound effect to achieve sustainable environmental goals along with economic growth path.

Lie symmetries and the constant elasticity of variance (CEV) model

The complete Lie symmetry analysis for a Financial model is presented. The problem with certain terminal conditions is considered. Exact solutions for such problems are derived. The concept of linearization of such equations is discussed.

NLRIS: Modeling and Analysis of Non-local Influence of Research Output of Institutions

In this paper, we posit a novel metric for ranking academic institutions based on the extent of influence their publications have on the global research community. We quantify the university’s global research impact using a calculated internationality score we call ’Non-local Research Influence Score’ (NLRIS). We propose the evaluation metric which is fair to the institutions which are smaller in size and do not qualify to be considered for the reputed ranking schemes but are performing well in terms of research quality and attracting citations and collaborators around the world. Our work calculates the scores of 75 universities using the Constant Elasticity of Substitution (CES) function. This score is calculated as a function of the global influence in terms of citations (Nonlocal Influence Quotient - NLIQ) and the extent of international research collaboration International Collaboration Ratio - ICR). The CES function accepts 2 variables, K and L as input and produces the variable Q as an output. In our model, we substitute K and L with the calculated values of ICR and NLIQ. The output of the CES function provides us with the desired internationality score of each institution. PSO is used to model the constrained optimization problem. In this paper, we also define a metric for representing NLIQ and ICR of individual universities. We have also performed a comparison between QS ranking and our calculated internationality scores.

The Relationship Between Production Inputs, Factor Substitution, and Economic Growth

Factors of production and elasticity of substitution play an essential role in economic growth accounting. Although production functions with constant elasticity of substitution between factors are more commonly utilized in growth accounting, studies based on production functions with variable elasticity of substitution are also conducted. Since production functions with variable elasticity of substitution provide more flexibility in parameters, they are more advantageous than other production functions. Besides, most studies focus on the elasticity of substitution between capital and labor. Studies on the sub-components of production factors are relatively few. In this study, capital stock is analyzed by dividing it into two subcomponents as public capital stock and private capital stock. The empirical results, in general, show that the elasticity of substitution between the public capital stock and the private capital stock is less than unity. In this context, public and private capital stock can be expressed as complementary inputs in the final production of goods and services. As a result, public expenditures on infrastructure can boost economic growth by raising the efficiency of private investments.

Optimal DC pension investment with square-root factor processes under stochastic income and inflation risks

ABSTRACT This paper studies optimally defined contribution (DC) pension investment problems under the expected utility maximization framework with stochastic income and inflation risks. The member has access to a financial market consisting of a risk-free asset (money account), an inflation-indexed bond, and a stock. The market price of volatility risk is assumed to depend on an affine-form, Markovian, square-root factor process, while the return rate and the volatility of the stock are possibly given by general non-Markovian, unbounded stochastic processes. This financial framework recovers the Black–Scholes model, constant elasticity of variance (CEV) model, Heston model, 3/2 model, 4/2 model, and some non-Markovian models as exceptional cases. To tackle the potentially non-Markovian structures, we adopt a backward stochastic differential equation (BSDE) approach. By solving the associated BSDEs explicitly, closed-form expressions for the optimal investment strategies and optimal value functions are obtained for the power, logarithmic, and exponential utility functions. Moreover, explicit solutions to some special cases of our portfolio model are provided. Finally, numerical examples are provided to illustrate the effects of model parameters on the optimal investment strategies under the 4/2 model.

Closed-form formula for conditional moments of generalized nonlinear drift CEV process

This paper studied a generalized case of the constant elasticity of variance diffusion (CEV) process whereas the drift term is substantially nonlinear in the short rate. Well-known instances deduced by this process are the extended Cox–Ingersoll–Ross (ECIR) process and the extended inverse Feller (EIF) process or 3/2-stochastic volatility model (SVM). We found particular sufficient conditions of existence and uniqueness of a positive pathwise strong solution for time-dependent parameter functions, and obtained closed-form formulas for conditional moments based on Feynman–Kac theorem. The accuracy and validity of the formulas were further investigated based on Monte Carlo simulations.

On Joan Robinson’s Output Symmetry Theorems with Various Taxations under Third-Degree Price Discrimination: A Generalization

This paper incorporates more general cases with a new class of constantly adjusted concavity demand curves and includes three types of taxes. To verify the output symmetry under various forms of taxation, we simulate both linear and constant elasticity demand functions under the unit, demand ad valorem, and cost ad valorem taxes. If all the demand functions in the submarkets are linear, the total outputs are identical under both uniform pricing and third-degree price discrimination. Furthermore, if all the weak market demand curves are strictly “Robinson-concave” and all the strong market demand curves are strictly “Robinson-convex” or linear, then the total output under price discrimination exceeds that under uniform pricing, and vice versa. While different taxes lead to higher costs, the cost pass-through changes the prices of the products, and the change of total output still depends on the curvature of the demand curve. Therefore, the curvature of the demand curve remains the main determinant of changes in output. Our study provides a theoretical basis for market intervention in price discrimination.

Gradual Stress-Relaxation of Hydrogel Regulates Cell Spreading.

There is growing evidence that the mechanical properties of extracellular matrices (ECMs), including elasticity and stress-relaxation, greatly influence the function and form of the residing cells. However, the effects of elasticity and stress-relaxation are often correlated, making the study of the effect of stress-relaxation on cellular behaviors difficult. Here, we designed a hybrid network hydrogel with a controllable stress-relaxation gradient and a constant elasticity. The hydrogel is crosslinked by covalent bonds and dynamic peptide-metal ion coordination interactions. The stress-relaxation gradient is controlled by spatially controlling the coordination and covalent crosslinker ratios. The different parts of the hydrogel exhibit distinct stress-relaxation amplitudes but the have same stress-relaxation timescale. Based on this hydrogel, we investigate the influence of hydrogel stress-relaxation on cell spreading. Our results show that the spreading of cells is suppressed at an increasing stress-relaxation amplitude with a fixed elasticity and stress-relaxation timescale. Our study provides a universal route to tune the stress-relaxation of hydrogels without changing their components and elasticity, which may be valuable for systematic investigations of the stress-relaxation gradient in cell cultures and organoid constructions.

Algebraic solutions for pricing American put options under the constant elasticity of variance (CEV) model: Application of the Lie group approach

In this work, the algebraic properties of the American put option under the constant elasticity of variance (CEV) model of financial markets are studied with the implementation of the symmetry approach based on Lie’s group theory. The CEV model is described mathematically in terms of the parabolic time–space partial differential equation (PDE) along with the suitable choice of a terminal condition. The classical Lie symmetry analysis is carried out for the governing PDE. Based on the infinitesimal Lie symmetry generators, new classes of group invariant solutions are derived from the mathematical model and the general as well as the specific cases of the CEV model are thoroughly examined. Finally, the results are plotted against the various emergent parameters and their effect are analyzed and discussed.

Health Care Provider Networks: Are Insurers Better Off?

Abstract Certain health insurers offer a free choice of providers and an identical copayment regardless of the provider. Others build networks and use selective contracting and financial incentives to channel policyholders to contracted suppliers. In the case of unregulated prices, we compare these two policies when the off-network medical service is not covered. We show how policy ranking depends on the characteristics of demand. If demand is linear, a for-profit insurer and a not-for-profit insurer obtain a higher profit and utility under selective contracting than under uniform reimbursement. In the constant elasticity case, these results do not hold. Insurers prefer uniform reimbursement while consumers are better off under selective contracting in both cases.

Impact Assessment of Non-Radical Innovations on the Efficiency of a Higher Educational Institution (on the Example of Southwest State University)

Relevance. Growing competition, including in the field of higher education, generates a demand for economic models that explain the factors in the formation of competitive advantages and predict the impact of non-radical innovations on prices, student recruitment and financial results.The purpose is development of a Cournot model of oligopoly competition in conditions of constant price elasticity of demand and its application to the regional higher education marketObjectives: development of a Cournot oligopoly model with constant elasticity of demand; computer modeling at different values of the marginal costs of oligopolists; application of the model to the higher education market and finding the value of the marginal cost of training an additional student; calculation of the value of the market elasticity of the training of architects; finding the expected forecast values of prices, the number of enrolled students and financial results.Methodology. The article was prepared within the framework of the positivist paradigm and the adductive approach, using the methods of mathematical modeling, comparative statics and economic analysis.Results. A model of oligopolistic competition in terms of output volumes for a situation of constant elasticity of market demand has been built; shows the impact of the introduction of non-radical innovations on economic efficiency in the context of changes in exogenous variables; calculated the value of elasticity in the regional market of educational services in the direction of "Architecture", and also the marginal costs of training a student in the direction of "Architecture"; forecasted changes in financial results in SWSU and KSU as a result of the introduction of nonradical innovation.Conclusions. Application of the model to the regional market of higher education (admission of bachelors in faculty "Architecture" at SWSU and KSU in 2020) showed the planned increase in the market share from 10,3% to 12,4% as a result of the introduction of non-radical innovations, which led to a 13% decrease radical costs. The projected increase in the net income of the innovator's organization will be from 21,2% to 49,2% in the regional higher education market ("Architecture").