Specific Functional Form Research Articles

Using Subsidies, Fines, and Restitution with Budget Balance to Combat Digital Piracy

Despite utilizing technical prevention methods and enacting copyright protection legislation, digital piracy has remained a persistent problem. We examine policy remedies to digital piracy whereby the policymaker has to balance its budget between fines on detected pirates, subsidies for legal purchases, and restitution to the firm. In our model, users choose whether to subscribe, copy, or not use the good, a firm decides on subscription fee and quality, and a policymaker determines subsidies, fines, and restitution. We find that the firm’s subscription fee is always increasing in subsidies, fines, and restitution under a budget balance constraint. The impact of these policy instruments on the firm’s investment in quality depends on how user marginal utility is influenced by the quality of the good and how the policymaker redistributes fines back to society, if at all. Using two specific functional forms with additive and multiplicative utility, we explain how these factors come into play. With additive utility, fines increase the firm’s investment in quality. However, with multiplicative utility the firm’s investment in quality decreases with fines if fines are used alone or alongside subsidies. In contrast to prior research, findings of our general framework illustrate that imposing fines on detected pirates “can” be socially optimal when accounting for the policymaker’s budget balance. Our specific functional forms also serve as two instances where imposing fines is always welfare maximizing. Finally, we find that although the policymaker’s optimal intervention improves social welfare and mitigates digital piracy, it leads to a reduction in consumer surplus. This paper was accepted by Hemant Bhargava, information systems. Funding: This work was supported by the Social Sciences and Humanities Research Council of Canada [Grant 435-2016-0431]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2021.03463 .

Analysis of initial singularity admitting viable bounce models

This research investigates the non-singular cosmic bounce models corresponding to Bianchi type-I spacetime in the framework of symmetric teleparallel theory. A specific functional form of this modified theory is used to examine the dynamics of bouncing cosmology. This study formulates the modified field equations and considers various parametric values to obtain feasible solutions. We examine the behavior of different cosmic bounce models corresponding to different scale factors and Hubble parameters, which resolves the big bang singularity as these parameters support the cyclic universe, there is a transition from an earlier contraction phase to another expansion phase. Furthermore, we investigate the behavior of energy density and pressure to comprehend the attributes of dark energy. The comprehensive analysis of equation of state parameter is also studied to determine the evolutionary eras of the universe. Our results indicate that the symmetric teleparallel theory describes cosmic expansion near the bouncing point.

Statistical inference and neural network training based on stochastic difference model for air pollution and associated disease transmission

A polluted air environment can potentially provoke infections of diverse respiratory diseases. The development of mathematical models can study the mechanism of air pollution and its effect on the spread of diseases. The key is to characterize the intrinsic correlation between the disease infection and the change in air pollutant concentration. In this paper, we establish a coupled discrete susceptible–exposed–infectious–susceptible (SEIS) model with demography to characterize the transmission of disease, and the change in the concentration of air pollutants is described in the form of the Beverton–Holt (BH) model with a time-varying inflow rate of air pollutants. Considering the periodic variation characteristics of data, time-varying parameters are defined as specific functional forms. We estimate the change point at which the parameters switch and the parameter values within the switching interval based on Bayesian statistical theory. The data fitting of the model can reflect the seasonal peaks and annual growth trends of values of air quality index (AQI) and the number of influenza-like illnesses (ILI) cases. However, the bias in data fitting indicates a more complex correlation pattern between disease and pollutant concentration changes. To explore unknown mechanisms, we propose the extended transmission-dynamics-informed neural network (TDINN) algorithm by combining deep learning with difference equations and obtain the curves of the transmission rate and inflow rate functions over time. The results show that neural network models can help us determine time-varying parameters in the model, thereby better reflecting the trend of data changes.

Interacting models of dark energy and dark matter in Einstein scalar Gauss Bonnet gravity

We study the dynamics of the interacting models between the Gauss-Bonnet (GB) coupled scalar field and the dark matter fluid in a homogeneous and isotropic background. A key feature of GB coupling models is the varying speed of gravitational waves (GWs). We utilize recent constraints on the GW speed and conduct our analysis in two primary scenarios: model-dependent and model-independent. In the model-dependent scenario, where determining the GW speed requires a specific GB coupling functional form, we choose an exponential GB coupling. We adopt a dynamical system analysis to obtain the necessary constraints on the model parameters that describe different phases of the universe and produce a stable late-time accelerating solution following the GW constraint, and find that to satisfy all these constraints, fine-tuning of the free parameters involved in the models is often needed. In the model-independent scenario, the GW speed is fixed to one, and we construct the autonomous system to identify the late-time stable accelerating critical points. Furthermore, we adopt a Bayesian inference method using late-time observational data sets, including 31 data points from cosmic chronometer data (Hubble data) and 1701 data points from Pantheon+ and find that all the observational constraints can be satisfied without fine-tuning. In addition, we also utilize simulated binned Roman and LSST data to study the evolution of the universe in the model-independent scenario. We find that the model shows significant deviation at higher redshifts from ΛCDM and fits the current data much better than ΛCDM within the error bars.

A Revealed Preference Test for Choquet and Max-Min Expected Utility with Ambiguity Aversion

We develop a revealed preference test for the Choquet expected utility model with ambiguity aversion, which does not rely on specific functional form assumptions on the utility index. It is computationally efficient if the number of states is not too large, even for a large number of observations. This is a nice feature compared to other existing revealed preference tests for decision models with ambiguity. We illustrate the usefulness of our results by implementing our test on two experimental datasets from the literature, and we compare the empirical fit of this model to the subjective expected utility model. (JEL C91, D81, D91, G41)

Developing novel wormhole metrics in finsler-randers geometry using the barthel connection and osculating-riemannian method

In this research, we focus on modelling a wormhole using Finsler-Randers geometry. By applying the Barthel connection from the range of Finslerian connections, we have developed a new wormhole metric, termed the osculating Barthel-Finsler-Randers metric, through the osculating-Riemannian method within the Finsler-Randers framework. The fundamental field equations are formulated in terms of the obtained metric tensor characterised by η(r), which plays a pivotal role in characterizing the anisotropy of the model. To explore the application of Finsler geometry in addressing the existence of a wormhole, we adopt an exponential shape function. Further, in order to streamline the computational aspects of our analysis, and to discuss the effect of anisotropy effect of Finsler Rander geometry, we adopt a specific functional form for the anisotropic parameter η(r)=arn, where α is a constant with implications for the anisotropy, among various possibilities for η(r) a non-zero analytical component of vector field in Randers metric. In addition, we consider three distinct values for the exponent n = −1, 0, and 1 and subsequently, we proceed to develop two distinct models for each of these three values of n with constant and non-constant redshift function. We analyse the physical implications of η(r) on the energy conditions. Our results demonstrate the crucial impact of anisotropy on the stability and structure of wormholes, emphasizing the requirement of exotic matter under specific conditions. This research deepens the understanding of wormhole physics within Finsler geometry, shedding light on the theoretical frameworks essential for the existence and stability of these cosmic structures.

Note on fuel consumption in ocean container shipping: Bounds on fuel usage

This paper contributes to the literature by deriving upper and lower bounds on the fuel consumption in container shipping. The bounds are derived from sailing distances, port times, and the possible arrival times at ports/ the berth windows negotiated between the ocean carrier and the port operators. Crucially, the derived bounds can be used in conjunction with any of the common fuel consumption functions proposed in the literature. This latter is especially important since currently there is no consensus on a specific functional form for the fuel consumption function. The behavior of the bounds will be illustrated with numerical examples.

A simple load model based on hybrid mechanism and data-driven approach for district heating in building complex

Accurate prediction of heating loads in district heating systems is essential for the implementation of demand-driven heating. This work presents a novel heating load prediction model that is particularly suitable for complex multi-user buildings. The input characteristics of the model are established through the heat transfer mechanism, considering factors such as the cumulative impact of outdoor temperature and user demand (indoor temperature). The specific form of the heating load function is determined using the MLR-PSO (Multiple Linear Regression-Particle Swarm Optimization) method. Only the indoor and outdoor temperatures need to be provided for the model to calculate future heating loads. Practical engineering tests demonstrated that the model achieved normalized mean bias errors of daily loads between 4.98 % and 5.54 % across different heating seasons, with a minimum annual relative deviation of 0.75 % for annual loads. Additionally, the model helps guide the operation of heating systems. For example, during the 2021–2022 heating season, setting the target indoor temperature at 18 °C reduced weekly energy consumption by 15.3 % compared to the previous season. This approach may be employed to construct a simple load model for existing heating systems to accurately predict both short-term and long-term loads, providing valuable insights into the management and control of heating systems.

Existence of static wormhole solutions in [formula omitted] gravity

This study explores wormhole solutions by analyzing energy conditions within the framework of f(R,A) modified theory of gravity, which is derived from the inverse of the Ricci tensor. For this purpose, we consider a linear model, defined as f(R,A)=R+αA, where R denotes the Ricci scalar, α is the coupling parameter, and A represents the anticurvature scalar. We further introduce a specific form of shape function to examine the characteristics of energy conditions for the distribution of anisotropic matter. Moreover, we examine the behavior of shape function and energy conditions for both isotropic and barotropic matter content as well. Through the selection of suitable parameter values, it has been shown that energy conditions are breached in some specified regions, indicating the existence of exotic matter. The thorough analysis confirms the presence of wormhole geometries in f(R,A) gravity.

Extinction and stationary distribution of a novel SIRS epidemic model with general incidence rate and Ornstein–Uhlenbeck process

We propose, in this paper, a novel stochastic SIRS epidemic model to characterize the effect of uncertainty on the distribution of infectious disease, where the general incidence rate and Ornstein–Uhlenbeck process are also introduced to describe the complexity of disease transmission. First, the existence and uniqueness of the global nonnegative solution of our model is obtained, which is the basis for the discussion of the dynamical behavior of the model. And then, we derive a sufficient condition for exponential extinction of infectious diseases. Furthermore, through constructing a Lyapunov function and using Fatou’s lemma, we obtain a sufficient criterion for the existence and ergodicity of a stationary distribution, which implies the persistence of the disease. In addition, the specific form of the density function of the model near the quasiendemic equilibrium is proposed by solving the corresponding Fokker–Planck equation and using some relevant algebraic equation theory. Finally, we explain the above theoretical results through some numerical simulations.

Capturing the dilution effect of risk‐based grouping with application to COVID‐19 screening

AbstractWe investigate the problem of screening a large population for an infectious disease (i.e., classifying subjects as positive or negative) using group testing while considering important test and population‐level characteristics. Group testing, in which multiple samples are pooled together into a master sample and tested simultaneously, has the potential to significantly expand screening efforts, and, owing to the COVID‐19 pandemic, the topic has seen a surge of interest recently. In this paper, we construct optimal group testing designs that consider a heterogeneous population (i.e., with subject‐specific risk), imperfect tests, and while also modeling the dilution effect of grouping (a phenomenon in which the test accuracy of the master sample is affected by the concentration of the virus in the pool), which is often ignored in the literature. We conduct an exhaustive analysis under both a general dilution function and a specific (yet still calibratable) form of the dilution function. Our analytical results of the resulting challenging optimization problems unveil key structural properties that hold in an optimal solution, which we utilize to construct efficient solution schemes. We complement the analysis with two case studies, one on the screening of blood for the Hepatitis B Virus and the other on the screening of subjects for COVID‐19. Our results reveal significant benefits over current practices, individual testing, as well as prior studies that ignore the dilution effect. Such results underscore the importance of incorporating both test and population‐level characteristics into the modeling framework.

Standard Post-Keynesian investment functions and their demand regime: a comprehensive empirical estimation for France

The aim of this article is twofold. In a first step, we estimate a large variety of standard Post-Keynesian investment functions for France over the period 1979–2020 by rigorously following the original features of a theoretical macro-model of growth and distribution. In a second step, for each of these investment functions, we also assess the corresponding demand regime contributing to the current profit-led/wage-led debate. Our results show that the French economy seems to be wage-led. Besides, the intensity of the regime varies greatly with the specific form of the investment function under consideration.

Pointwise Nonparametric Estimation of Odds Ratio Curves with R: Introducing the flexOR Package

The analysis of odds ratio curves is a valuable tool in understanding the relationship between continuous predictors and binary outcomes. Traditional parametric regression approaches often assume specific functional forms, limiting their flexibility and applicability to complex data. To address this limitation and introduce more flexibility, several smoothing methods may be applied, and approaches based on splines are the most frequently considered in this context. To better understand the effects that each continuous covariate has on the outcome, results can be expressed in terms of splines-based odds ratio (OR) curves, taking a specific covariate value as reference. In this paper, we introduce an R package, flexOR, which provides a comprehensive framework for pointwise nonparametric estimation of odds ratio curves for continuous predictors. The package can be used to estimate odds ratio curves without imposing rigid assumptions about their underlying functional form while considering a reference value for the continuous covariate. The package offers various options for automatically choosing the degrees of freedom in multivariable models. It also includes visualization functions to aid in the interpretation and presentation of the estimated odds ratio curves. flexOR offers a user-friendly interface, making it accessible to researchers and practitioners without extensive statistical backgrounds.

DeepOTF: Learning Equations-constrained Prediction for Electromagnetic Behavior

High-quality passive devices are becoming increasingly important for the development of mobile devices and telecommunications, but obtaining such devices through simulation and analysis of electromagnetic (EM) behavior is time-consuming. To address this challenge, artificial neural network (ANN) models have emerged as an effective tool for modeling EM behavior, with NeuroTF being a representative example. However, these models are limited by the specific form of the transfer function, leading to discontinuity issues and high sensitivities. Moreover, previous methods have overlooked the physical relationship between distributed parameters, resulting in unacceptable numeric errors in the conversion results. To overcome these limitations, we propose two different neural network architectures: DeepOTF and ComplexTF. DeepOTF is a data-driven deep operator network for automatically learning feasible transfer functions for different geometric parameters. ComplexTF utilizes complex-valued neural networks to fit feasible transfer functions for different geometric parameters in the complex domain while maintaining causality and passivity. Our approach also employs an Equations-constraint Learning scheme to ensure the strict consistency of predictions and a dynamic weighting strategy to balance optimization objectives. The experimental results demonstrate that our framework shows superior performance than baseline methods, achieving up to 1700 × higher accuracy.

Policy Formulation for an Optimal Level of Savings in a Dynamic Setting

Objective: Previous literature on optimal savings relies on specific utility and production technology functional forms which might not be able to produce robust results as different utility / production functions may lead to dramatically different or opposing results. This paper derives an optimal savings policy based on parameters (such as slopes of demand and supply curves) which can be empirically estimated and provides a unique and robust result irrespective of shape and form of individual utilities / production functions. Furthermore, existing literature does not consider welfare loss when savings market is adjusting to final equilibrium after a shock while deriving an optimal savings policy. In addition to that, number of savers (all public and private saving entities, including households, firms, etc.) and saving rate are vital parameters for savings in an economy, and while deriving an optimal savings policy, it is necessary to take into consideration these parameters to ensure that quantum of savings due to interest rate movement gets adjusted in target time duration, without which there may be additional efficiency loss than that envisioned while deriving an optimal savings policy for an economy. Methods: This research project designs a dynamical model for savings market and extends that to a three-dimensional savings system in an economy by taking into consideration number of savers, saving rate, and interest rate; and based on that derives an optimal comprehensive savings policy while accounting for efficiency losses when savings market, saving rate, and number of savers are adjusting to final equilibrium, in addition to the welfare loss on account of equilibrium shift. Results: Without consideration of welfare loss / gain while savings market is adjusting after implementation of a savings policy, welfare picture remains incomplete, and the optimal savings policy based on partial welfare cannot be considered as optimal in true sense. Traditionally, welfare of only producer and consumer is taken into consideration without accounting for welfare of production factors. An expression of efficiency loss / gain as a result of savings policy based on welfare including those of production factors has been presented and optimal savings policies have been derived by minimizing efficiency losses and presented as a final result in the form of mathematical expressions. This paper demonstrates that both supply and demand shocks operate through a common channel, i.e., inventory of funds in savings market as both kinds of shock affect inventory of funds and hence can be categorized just as an inventory shock. Conclusion: For optimal welfare gains, practitioners / policy makers must estimate theoretically derived optimal savings policies based on the dynamic model developed in this paper and presented in the form of mathematical expressions from real world relevant data for implementation.

Special function form solutions of multi-parameter generalized Mittag-Leffler kernel based bio-heat fractional order model subject to thermal memory shocks.

The primary objective of this research is to develop a mathematical model, analyze the dynamic occurrence of thermal shock and exploration of how thermal memory with moving line impact of heat transfer within biological tissues. An extended version of the Pennes equation as its foundational framework, a new fractional modelling approach called the Prabhakar fractional operator to investigate and a novel time-fractional interpretation of Fourier's law that incorporates its historical behaviour. This fractional operator has multi parameter generalized Mittag-Leffler kernel. The fractional formulation of heat flow, achieved through a generalized fractional operator with a non-singular type kernel, enables the representation of the finite propagation speed of heat waves. Furthermore, the dynamics of thermal source continually generates a linear thermal shock at predefined locations within the tissue. Introduced the appropriate set of variables to transform the governing equations into dimensionless form. Laplace transform (LT) is operated on the fractional system of equations and results are presented in series form and also expressed the solution in the form of special functions. The article derives analytical solutions for the heat transfer phenomena of both the generalized model, in the Laplace domain, and the ordinary model in the real domain, employing Laplace inverse transformation. The pertinent parameter's influence, such as α, β, γ, a0, b0, to gain insights into the impact of the thermal memory parameter on heat transfer, is brought under consideration to reveal the interesting results with graphical representations of the findings.

Model-averaging as an accurate approach for ex-post economic optimum nitrogen rate estimation

AbstractFinding economic optimum fertilizer rate with good accuracy is essential for optimal crop yield, efficient resource utilization, and environmental well-being. However, the prevailing incomplete understanding of input-output relationships leads to imprecise crop yield response functions, such as those for winter wheat, and potentially biased fertilizer choices. From a statistical point of view, there is uncertainity with regards to which model is most suitable to estimate the economic optimum fertilizer rate. This complexity is amplified when considering site-specific nitrogen fertilization, which factors into elements like soil attributes, topography, and crop variations within a field, as opposed to uniform application. This study undertakes a comparative analysis to evaluate biases, variance, mean squared errors and confidence intervals in Economic Optimum Nitrogen Rate (EONR) estimations across different functional forms. The goal is to uncover performance discrepancies among these forms and explore potential advantages of adopting model averaging for optimizing nitrogen use in crop cultivation. The results of simulations reveal noteworthy biases when comparing diverse yield functions with the averaged model, particularly evident in the Linear-Plateau and Mitscherlich models. Moreover, analysis of empirical data indicates that confidence intervals for the averaged model overlap with the projected ranges of all functions. This implies that the averaged model could be suitable for determining EONR and effectively address the problem of model specification without focusing on one specific functional form. The effectiveness of model averaging hinges on incorporating models that well approximate the true model. However, even if the true model is not known, the average model can provide reasonable information for determining the EONR, provided that similar model specifications are considered. This has implications for modelling of yield response for various applications and can contribute to unbiased estimations of yield response.

A nonparametric random effects model for the valuation of forest recreation services: An application to forest sites in Tuscany, Italy

AbstractThis study assesses individuals' preferences for the use of forest sites for recreational purposes by means of the logit‐mixed logit (LML) model. The appeal of the LML is that the analyst does not need to assume any specific functional form for the mixing distributions of random preferences. The empirical analysis generates a data‐driven nonparametric representation of individuals' preference heterogeneity. We apply this approach to data collected using an unlabelled discrete choice experiment (DCE), consisting of three recreational options, two of which are in two hypothetical forest sites. Forest destinations are described by means of six attributes: forest type, signposting, hiking time, access to rivers or lakes, wildlife watch hides for visitors and cost of access. The empirical findings reveal that the signpost for each trail is the attribute for which respondents are on average willing to pay the most (6.565€). Further evidence suggests that respondents have strong positive preferences for those forest sites that offer amenities such as wildlife watching hides and access to rivers or lakes. Finally, the histograms derived from the semi‐parametric LML estimation reveal multimodality of random taste amongst respondents for different hypothetical forest sites.

A global model of intensity autocorrelation to determine laser pulse duration

We present a new global model of collinear autocorrelation based on second harmonic generation nonlinearity. The model is rigorously derived from the nonlinear coupled wave equation specific to the autocorrelation measurement configuration, without requiring a specific form of the incident pulse function. A rigorous solution of the nonlinear coupled wave equation is obtained in the time domain and expressed in a general analytical form. The global model fully accounts for the nonlinear interaction and propagation effects within nonlinear crystals, which are not captured by the classical local model. To assess the performance of the global model compared to the classic local model, we investigate the autocorrelation signals obtained from both models for different incident pulse waveforms and different full-widthes at half-maximum (FWHMs). When the incident pulse waveform is Lorentzian with an FWHM of 200 fs, the global model predicts an autocorrelation signal FWHM of 399.9 fs, while the classic local model predicts an FWHM of 331.4 fs. The difference between the two models is 68.6 fs, corresponding to an error of 17.2%. Similarly, for a sech-type incident pulse with an FWHM of 200 fs, the global model predicts an autocorrelation signal FWHM of 343.9 fs, while the local model predicts an FWHM of 308.8 fs. The difference between the two models is 35.1 fs, with an error of 10.2%. We further examine the behavior of the models for Lorentzian pulses with FWHMs of 100 fs, 200 fs and 500 fs. The differences between the global and local models are 17.1 fs, 68.6 fs and 86.0 fs, respectively, with errors approximately around 17%. These comparative analyses clearly demonstrate the superior accuracy of the global model in intensity autocorrelation modeling.

A categorization-modelling procedure to estimate urban goods transport demand with a minimum number of activity categories

This paper presents an integrated clustering-regression modelling framework to assess the number of trips that each establishment of a given urban zone, city or conurbation generates. The goal of the method is to construct establishment-based trip models using the categorial FTG methodology using a minimal set of categories of activities. The methodology combines a hierarchical cluster analysis that defines a limited number of coherent categories of activities, then a regression-based modelling method that links the FTG rates (production, attraction and generation) to employment, giving a specific functional form for each category (constant, linear, logarithmic or potential). The models are constructed and calibrated on the basis of the 2011-2012 Freight Trip Survey of the Paris Region. Using a hierarchical clustering technique, 5 categories of establishment are defined and resulting FTG models obtained. Most functional forms are linear or potential, with some particular cases where constant generation is preferred. Results are assessed using the R2 coefficient and discussed. The resulting models are robust and applicable to any French city.